Speaking specifically about The Beatles: it was generally the modern recording studio and more specifically the tape recorder. I'll leave the social commentary for someone else, but the technological change in recording was huge.
Imagine a world where a band had to be recorded in one take. Everyone had to play at the same time into either a one track wire recorder or into a variety of acetate discs. And they had to play at the right volume to mix different voices and sounds into the recording. There were even specialized instruments built to make it easier for violins to be recorded. Often the drums would be set across the room while a vocalist would be singing as loud as possible right into the microphone.
This began to change in the 1940s and 1950s with tape machines, which were first developed by the Germans in WW2. Now, you could both do multiple takes, as you could re-record over tape easily, where you cannot with acetate discs. Also, while one can splice together wire recorder tracks with very fine knots, tape was reasonably easy to spice and to change reels. (Wire recorders are awful, the wire is about the thickness of a stout hair and it must be moved much more quickly than a comparable tape, so they also are very difficult to reverse and had issues with spooling.) This allowed much easier editing and reuse of recording materials. No longer did a band have to directly records into acetate discs which were only good for one take.
The next huge step is the 'studio' as an institution. Part of the Beatle's success was access to the most modern studios of the day. These first studios were a multi million dollar investment, with some of the most complex analog sound manipulation gear ever produced. Later studios benefitted from advances in semiconductor, tube and tape technology, which cut down some of the cost and complexity for later groups.
Most of the Beatles music was recorded at 4 tracks (2 simultaneous stereo recordings or 4 mono recordings) on 1 inch tape, at something like 24 inches per second. By the 1970s 1/2 tape machines could do 8 tracks.
This has a great benefit, namely with two (or more) tracks a studio engineer could 'mix' together two different recordings onto one tape, which then could be mixed down to stereo or mono for use in producing the actual LP. This allowed the Beatles to add layers of complexity and novelty (sitars, horns, Yoko screaming, etc.) which were unthinkable to produce even 10 years earlier. Furthermore, the entire band did not have to be physically present, they could fight and not speak to each other, while still producing music. It became trivial to have 'do overs' for technically challenging sections. Ringo could come in, get the drum tracks done and leave. Then they would play that track for Paul and he could record his guitar riff and some vocals. Then George could come through and play some sitar, etc. If something was 'off' then you could get that person back in the studio to record a new version. They could even radically change the composition of a song.
The Beatles could not actually perform any of their music live after say Revolver, because it had become too complex and dependant on recording technology. Indeed on their last US tour (and the final paid live performances of the Beatles) they did not play any material from Revolver, despite the LP having been released a few days before the start of the tour.
Sources: The Beatles Encyclopedia: Everything Fab Four, Ken Womack
www.obsoletemedia.org/wire-recording/
www.theaudioarchive.com/TAA_Resources_Disc_Transcription.htm
There has been a continual stream of new pop acts that the British record companies have been trying to push to British fans since, basically, the days of music hall and the start of the British record industry. Each week, there are new acts that get onto the record sales charts, and they have done so since the first charts in the mid-1950s (when such charts started to be published in the UK).
So what we're talking about here is the process by which some of these acts, plucked out of this continual stream, eventually become 'immensely influential'. What does it mean to be immensely influential? Usually, it means that other bands want to sound like them, and that people keep talking about them years later; their music doesn't keep floating past us in that continual stream of pop (as the majority of pop does), but manages to get stuck on the shore of pop culture in some way.
It should be pointed out that the Beatles first hit some popularity in the UK at the end of 1962 and at the end of 1963 in the US, while Queen first had top 10 hits in the UK in 1974, and first had a hit in the US with 'Bohemian Rhapsody' in 1975. And the reason it should be pointed out is that, previous to The Beatles, it was relatively unusual for British musicians to break into the American charts, but by the time Queen had an American hit with 'Bohemian Rhapsody', over a decade later, it was relatively run of the mill.
So what happened in the UK? Well, nothing in particular, except that the Beatles were in the right place at the right time. The key here is the demographic explosion of the baby boomer generation, who wanted music that reflected their lives and their times. The enormous amount of (white) baby boomers who were born in the late 1940s and early 1950s were teenagers by the time that the Beatles broke into popularity; they were too young, in general, for the rock'n'roll of the 1950s, but they wanted music that reflected the electricity of the lives they were born into (in an era where electrical appliances were widely available to white suburban families for the first time) and they wanted music that had the same youthful vigour and which had something of the incipient sexuality that they felt as teenagers.
However, the record companies of the early 1960s were generally rather conservative and uninclined to put more energetic, raw sounding music out, with the more conservative record labels typically having wider reach and more power. The Beach Boys in 1962-1963 and the Beatles in late 1963 in America were the first relatively raw-sounding rock'n'roll bands to receive a dedicated promotional effort by a major record label like Capitol in some time, and The Beatles became such a phenomenon that American record labels mined their British counterparts for material, which promptly also shot up the charts (partly because in the wake of the Beatles, their competitors as rock'n'roll bands in Liverpool and elsewhere in the UK were all very promptly signed up to record labels).
So there was a deep interest in British bands during what was a pivotal time in the formation of tastes amongst American baby boomers. It also took the American record industry a surprisingly long time to find and promote American bands that could compete with the British rock'n'roll bands; 'Mr Tambourine Man' by the Byrds, for example, was released in June 1965. This was because the American record industry were in part still hamstrung by the conservative music industry attitudes about how pop music should sound (which were now, clearly, outdated). As a result, a set of British bands from 1963-1965 - The Beatles, The Rolling Stones, The Kinks, The Animals, etc - were given a platform in America which they exploited artfully, before there was a resurgence of homegrown American product that was influenced by the Beatles and their huge success (The Byrds, Bob Dylan's rock stuff, The Monkees, The Byrds etc.).
The other issue here was the issue of race, of course; Elvis Presley in the 1950s had become a star by being a hillbilly who was singing black music; the Beatles in the 1950s in England were only dimly aware of the racial issues surrounding rock'n'roll in the 1950s, in an era where there was little rock'n'roll on music television (especially British television), and where 7" rock'n'roll records often came without a cover image. So The Beatles - who were of course, a few years older than their fans, being born during World War II rather than afterwards - were fans of 1950s rock'n'roll, and they were often unaware if the acts they liked were white or black; what appealed to them was energy. In being English and thus somewhat disconnected from issues of American segregation and stereotypes about African-America sexuality, the Beatles could get away with a level of energy and sexuality in their music which would not have been as welcome in pop culture from an African-American band, and which a white American band might have been more reticient about.
After The Beatles and the 'British Invasion' of 1964-1965, the British record industry also developed a new confidence and a new willingness to experiment (both with technology, drugs, styles, and sounds), which stood them in good stead as American baby boomers themselves developed a new confidence and a new willingness to experiment. Queen actually, in some ways, represent the point where the British pop industry and American tastes start to diverge; the glam rock explosion of the early 1970s in the UK - which Queen initially tagged themselves onto - was nowhere near as popular in the USA; T.Rex had more than ten top 5 singles in the UK, and only 'Get It On' reached the top 10 in the USA. And Queen, through the 1970s, were much more successful in the UK than in the US; it was only with 'Another One Bites The Dust' in 1980, a sort of disco song, that they actually had a #1 single in the US; 'Bohemian Rhapsody' did better in the US charts in 1992 when re-released after Freddie Mercury's death around the time it was prominently used in Wayne's World, than it did when it was a new song in 1975.
Additionally, the demographic explosion of the baby boomers also continued to think the music they liked as teenagers was important and influential. The baby boomers were the ones who wrote the history of rock music in music magazines and books, and who directed the documentaries about how important rock was. Unsurprisingly these baby boomers focused on 'their' music, and their own experiences of that music and why it was important. So the British bands they liked in 1964 and 1965 became a pivotal part of the story of rock, and the Beatles' continued influence got turned into something epochal.