B:TAS was developed during a time when animation was starting to be viewed as more "mature". Something that all people could enjoy rather than as something that was "just for kids". The Simpsons came out only a few years before, ushering in an era of mainstream adult animation that grew in the 1990s with stuff like Beavis and Butt-Head and South Park, and continues to this day. The Disney film Who Framed Roger Rabbit was developed by Steven Spielberg and Robert Zemeckis, two of the biggest names in the film industry. Its success helped launch the Disney Renaissance, where films like The Little Mermaid and Aladdin became mainstream hits. Beauty and the Beast became the first animated film to ever receive an Academy Award nomination for Best Picture. For the first time in decades, animation was "cool".

Which brings us to the development of B:TAS. The series was primarily influenced by Tim Burton's 1989 film "Batman" and its 1992 sequel "Batman Returns". When viewed through a modern lens, they may not seem all that special today, but at the time they were viewed as fairly revolutionary. In the 1980s, when people thought of Batman they thought of the campy 1960s show with Adam West, or the Super Friends cartoon. The Burton films basically reinvented Batman in the public consciousness, and are the prototype of the modern "dark/gritty" superhero films we see today. In the B:TAS series bible, they take note of saying "The humor in our version of Batman should arise naturally from the larger than life characters and never from tongue-in-cheek campiness". There was a concerted effort by the showrunners to not be "just another silly cartoon". This was designed from the outset to be a more mature work. There wasn't going to be any "Holy Swiss Cheese, Batman!" in this. In fact, B:TAS actually drew their backgrounds onto black paper in order to enhance that darker, noir aesthetic they were going for.

Which brings us back to why the show was viewed as so revolutionary. B:TAS was arguably the first Western animated series to put focus on long-form storytelling. Previous cartoons had certainly had "story arcs", but for the most part they made up maybe a few episodes in a row where the characters would all go on a little adventure and then revert to the status quo. That was not the case in B:TAS. Everything that happened mattered, and it continued to matter as the series moved forward. For the first nine episodes of the series, Harvey Dent is just the DA of Gotham. There's an entire episode dedicated to him. He shows up a few times as nothing more than the DA. But then in the 10th episode of the series, he becomes Two-Face. And that's how he stayed for the rest of the series. There was no going back to the status quo. A recurring character and ally to the main character was traumatically disfigured and became a villain. That was pretty much unheard of in animation up to that point. Compare that to something like the 1980s Transformers cartoon. Infamously, in the 1986 film "The Transformers: The Movie", the character Optimus Prime is killed. This was so upsetting to younger viewers and garnered such a massive backlash among audiences that he was revived in the cartoon later on. That kind of thing didn't happen in B:TAS.

This focus on a continuous story and the success of the series led to the creation of more animated series. In 1996, Superman: The Animated Series came out, and it featured several crossovers with B:TAS. A year later, B:TAS was continued with The New Batman Adventures (though this is often viewed as just another season of B:TAS despite the new title/art style). This was a direct continuation of the original series where time had clearly passed. Dick Grayson (Robin) had now become the superhero Nightwing, and was no longer Batman's sidekick. There was now a new Robin, Tim Drake. Barbara Gordon had become Batgirl. The story had clearly advanced in a way that just wasn't seen in animation prior to this. This led to Batman Beyond, and Justice League, and other animated series that are now referred to the "DCAU" (DC Animated Universe).

The DCAU was essentially the prototype of the modern cinematic universe as we understand it today. Every show impacted the other. Characters would appear in one episode of one show, then later on they'd appear in another show. Everything that happened had an impact down the line. As an example, look at the character of [Ace](https://dcau.fandom.com/wiki/Ace_(metahuman)). They first appeared in an episode of Justice League as a member of the "Royal Flush Gang", and then in an episode of Justice League Unlimited. I'd prefer to not get too in depth into the story, but basically, this one character appears in two episodes across the entire DCAU, but their impact was felt across multiple shows, by numerous characters, and across multiple decades of the in-universe story.

When people call B:TAS influential, this is what they're talking about. The show revolutionized how cartoons were written. Go to any list of "Best Cartoons Ever". What are you going to find? Cartoons with long-form, ongoing stories that last the entire series. Avatar: The Last Airbender. Adventure Time. Gravity Falls. That style of cartoon was basically invented by Batman: The Animated Series. I don't think it's an exaggeration to say that there wouldn't even be a Marvel Cinematic Universe had Batman: The Animated Series not paved the way decades beforehand.

And that's not even getting into how it influenced the Batman mythos. Harley Quinn was invented for B:TAS. Mr. Freeze's backstory as trying to save his wife from a deadly disease was invented for B:TAS. Terry McGinnis was invented for Batman Beyond. Voice actors Kevin Conroy (RIP) and Mark Hamill are to this day considered by many to be the definitive actors for Batman and the Joker, continuing to voice them in various projects to this day. It really can't be overstated how influential B:TAS was.

You asked about innovation/new techniques, and fittingly for an animated show, they took great pains with the visual design.

The most striking of these reinforced the bold "Dark Deco" art style that made Batman: The Animated Series instantly recognizable at a glance: it was drawn on black paper instead of white, which had never been done before in a television production. As Eric Radomski, show co-creator and background painter, pointed out, "For animation, I don’t recall anyone ever doing that, other than maybe Mary Blair experimenting with some Disney short films. What we were doing was literally trying to interpret the night with an impressionist style. If we did it wrong, it was going to look like the black-velvet paintings that were popular in the ’60s and ’70s."

Bruce Timm, show co-creator and director, made another stylistic choice that helped TAS stand out: "There’s no good reason to draw every shoelace on a shoe. Just make it a simple shape. That was Eric’s and my basic idea for the entire series, to simplify everything. The characters and the vehicles and the props and the cars and everything — just boil everything down to its essential ingredient." This was a reaction to other action-adventure cartoons Timm had worked on: "[E]very single one of them, I thought, was overdesigned. They were trying to impress people with the amount of detail. On G.I. Joe, especially, it wasn’t enough just to draw a belt on a character, the belt had seams and buttons and snaps and pockets. ... We both were big fans of the Fleischer Studios cartoons from the 1940s. It was a combination of that and film-noir movies and things like Citizen Kane."

Aurally, the show stood out via another unique tactic: they hired Shirley Walker, a composer who had worked with Danny Elfman on the first Batman film, who in turn brought on dozens of other composers, and in what Timm called "a huge plus" that was "almost unheard of" at the time, they scored every episode of the show.

They also cast a wider net when looking for voice actors, hiring a Juilliard-trained stage actor to play the title role rather than a known voice actor; it was Kevin Conroy's first-ever voiceover role.

Sources: Vulture's excellent "An Oral History of 'Batman: The Animated Series'" -- which you should absolutely read if you have any interest in TAS at all -- and "The Scores of 'Batman: The Animated Series'".

The show functions as a kind of marker between the era of broadcast network "Saturday morning" animation and children's programming and the era of animation that was not just for children and that aired on a wider variety of cable channels and time slots. It earns that status in part because of its distinctive aesthetics, in part because of its historical moment.

On the historical moment, by the early 1990s, the ecosystem of American children's visual culture had already gone through two major shifts. First, the rise of cable and the addition of Fox as a fourth broadcast network had eroded the traditional dominance of the three major American networks and with it, the stultifying authority of the networks' Standards and Practices offices that had grown considerably during the 1980s in response to complaints about the over-commercialization of children's programming that was tied closely to toy lines like He-Man or G.I. Joe. Cable generally offered a less regulated content environment, and to some extent, the parental watchgroups that had such an intense focus on television in the 1970s and 1980s had lost some of their steam for a variety of reasons.

Batman: The Animated Series wasn't the first animated program on television to take advantage of a more relaxed environment--to some extent it followed in the wake of much more aggressive challenges to the old regulatory regime like Mighty Mouse: The New Adventures and its spiritual sequel, Ren & Stimpy (appearing a year before B:TAS), or the non-animated Pee-Wee's Playhouse. Mighty Mouse was also a harbinger of the arrival of a wider variety of animation styles in children's programming (Doug and Rugrats appeared in the same year as Ren & Stimpy), which BTAS also exemplified. As creators who had grown up on Saturday Morning programming but who had greater visual and narrative ambitions than the cheap and repetitive approach that predominated in the 1970s and 1980s began to trickle into television production, they were ready to move assertively into the space left by the retreat of older network broadcast standards.

BTAS didn't push the same kinds of frontiers as Ren & Stimpy and a number of other shows appearing in the early 1990s, and it certainly had some significant constraints imposed on its content (notably in how the creators were constrained in their reference the murder of Bruce Wayne's parents, but also in a series of "thou shalt nots" that they later parodied in a single drawing) but the difference to long-time viewers felt like night and day. Not just in the relative sophistication of the story-telling and characterization but also in the stylized visual aesthetic of the program communicated forcefully from the get-go in the title sequence.

In terms of the OP's question, that really did feel revolutionary if you'd grown up watching much more heavily controlled cartoons where at one point the only approved message that S&P offices would allow was very nearly "it's good to cooperate with other people!" Compare BTAS to something like the first two seasons of Super Friends from the 1970s, which were barely allowed to show super heroes having any conflicts with antagonists of any kind--and which were made on the lowest budget possible with very simple visual backgrounds.

But given that children's programming had largely existed as a way to keep kids busy on weekend mornings and afterschool and to sell products to them, you might ask "Why was there a whole new wave of higher-quality animation and programming directed at children? Why were creators allowed to make fundamentally better work?" And that's the second change that made BTAS a good marker of a major shift in American popular culture. In 1989, Disney's The Little Mermaid was a major commercial success only four years after a notorious flop, The Black Cauldron. What changed? Most notably, The Little Mermaid managed to appeal to both adults and children, rather than being something that adults resentfully sat through as caretakers for children in the audience.

That catalyzed an entire generation of film and television producers in a way that now seems entirely commonplace to current audiences but at the time felt like a major transformation of the cultural marketplace. Sure, there were still programs that were marketed entirely to young children and certainly there was still a good deal of entertainment considered appropriate only for adults, but suddenly many families (and even people without children) felt comfortable watching programs and films that offered something to everyone in the audience. The same generation that grew up loving comic books and animation, or that watched films like Star Wars, was also ready to share more of the same with their own children, as opposed to their parents, who had been raised to leave child-like popular culture behind them.

So BTAS didn't do any of this by itself--arguably there are a few programs that took even bigger risks and forged the path first--but it is a memorable, distinctive marker of the transition to cable and the erosion of network control over popular culture as well as a marker of the moment where a new generational audience was ready to break down the walls between kidvid and entertainment for adults.