I'm hoping this answer will meet all the reqs of the sub and answer your question. It won't be as long as some others here, but hopefully valuable.

'Riverdancing' is, of course, the cultural art of Irish Step Dancing. You're not really asking about the history of the dance form, but just as a bit of a precis- there are times it's been very, very controversial. I'm sure you're quite aware of England's history of viewing Ireland, both North and South, as their back garden, with the Irish not always agreeing. Think of it something like the Scots and their tartans- during times when invaders have attempted to suppress the people, one of the first things they go for are expressions of culture. This was especially pronounced in the 'Penal Days', a 400 year period around the 1600s where a huge attempt was made to crush all Irish industry, culture etc, so all sorts of cultural expression got driven 'underground'. However, we do have some recorded 'Irish Dance Masters' from about 1750s forward (Gaelic Revival), suggesting some formal acknowledgement of Irish dance.

Of itself, it is a pretty standard folk dance. Using primarily jig and reel rhythms, often with 'set dances' tied to specific folk melodies, themselves usually crafted from folk story (Gates of Derry is a good example of a set dance using a folk tune based on myth). Most people who don't know much about Irish dance picture the solo stuff, but there's a deep and rich history of the 'ceili', or team dancing, again very like the Scots have.

In Ireland itself, pre-Riverdance, it thrived- but in the way cultural dance 'thrives' around the world. There was a rich competitive scene, culminating annually in the 'Worlds', or Oireachtas Rince na Cruinne, organized by An Coimisiún Le Rincí Gaelacha, currently the world's largest body for Irish dance in its competitive form. The CLRG as it's known, stems from 1927, and was founded as a direct effort to unify all the separate interests vying to culturally re-promote Irish heritage (and at one point language). Competition-wise, this is where we see the (now dated) 'boxy' dresses + sash, or pants and band for men, evolve as a competition standard, with teams wearing matching uniforms and solo dancers 'earning' their way from the studio dress to their soloist's colors as they level. If you're familiar with the Lord of the Dance lineup, those are the costumes they're directly mocking in the number 'Breakout'. Of course, not all dancing was competitive, I'm less qualified to speak there, but your ma and pa may, more informally, go down the pub and dance one of those sets or ceilis for fun to the band. Maybe granddad would pull out his spoons to accompany the band. Sundays the bowling club or similar may throw a ceili for folks to come dance.

These are, of course, not the things that make you cool as a kid at school or get much press time. That's what Riverdance would change. Suddenly the slightly uncool thing you all did extracurricular but never mentioned became a flashy and, dare we say, sexy Broadway show with lights and colors and costumes. They kept the tin whistle and drum and fiddle, but they made the rhythms more enticing, more modernized. And it caught the world's attention because it was novel, it was powerful, and, if I can offer a personal opinion, it was INCREDIBLY well done- a lineup of world champs, an intensely lauded choreographer, exceptional music, Anuna's exceptional voices. It was also well timed, with the Celtic Tiger economic boom in full swing. It likely helped that it was the interval act for the Eurovision awards, which had their own cheesy legacy of cultural celebration people didn't expect to see broken, so it also imparted the single number ('Riverdance' the breakthrough phenomenon was just the single dance number, the show came later) a lot of punch when it turned out to be cultural, yes, but slick and produced and glamorous instead of the usual less budgeted options.

From there, it gained social traction. They remade the single number into a show. Miles Copelands' track record as a Broadway Manager, built up from marketing Sting and the Police, helped. So did many other things.

To cut a long story short, they had a lot of theatrical luck and did the right thing at a time the world was ready for it. A star cast, choreographer, crew and promoters. At a time when the 'Celtic Tiger' economic boom in Ireland (a different subject I am not as qualified to comment on) was starting to accelerate, reawakening both interest and patriotism and pride in Irish heritage- a pride especially amplified in America, with a rich history of Irish immigration. With traction in America, you have access to 'Hollywood' theatricality.... big name promoters, big name venues, access to Broadway etc. With Flatley's later split to make the EVEN sexier, EVEN 'bigger', EVEN flashier Lord of the Dance...and his talent for showmanship brought to major fruition, you had the perfect recipe for capturing the public's attention at a time they were looking for something interesting, and preferably Irish (again, the 'Celtic Tiger')

As a young dancer myself right at that time, let me tell you- it was SO refreshing to finally be 'cool'. My geeky competitive weekends were suddenly of interest to schools for colors. Pubs and other venues wanted SHOWS, not 3 renditions of Blackthorn Stick done as boringly as possible. Shoes, wigs, costumes all got better. There was massive influx into studios worldwide- today the CLRG overseas the competitive circuit in 26 countries, including Asia and South Africa, which primarily got their start through existing dance teachers (highland or ballet, often, but not exclusively) training to teach Irish step dancing. We're now into a second gen (including myself) who seek these qualifications out directly.

Of course, the Broadway boom (and the 'Celtic Tiger') fizzled out, and the next greatest thing came along, but the reinvention in Irish dance has stuck. There's more studios globally, in more countries, than ever before. The competition circuit is fierce. Dancers can still find many Irish dance shows in theater circuits worldwide to employ them. As a non-dancer you probably don't hear about it much, but if you are a dancer, the legacy of the reinvention of Irish dance definitely lives on- we're just back to the global point where the World Champs get a line or two in local newspapers IF local dancers are competing.

Some research sources you may enjoy:The changes in Irish Dance since Riverdance

Perceptions of Irish Dance locally and globally

An exploration of Irish Dance through Trauma Theory (this gets into it as an expression of culture)

Contemporary Irish Choreographers and Cultural Identity

Irish Dance during the Gaelic Revival

Entertainment in Independent Ireland

I do have some basic sources on the Penal Years and the Celtic Tiger boom, but I am in no way a scholar of either- it's the history of the dance I used to compete in that I love- so I would rather let some folks with better sources speak for those.

Riverdance was the name of an Irish dancing show that was performed at the 1994 Eurovision Song Contest, and which starred the American dancer Michael Flatley. There are a few factors which combined to make this performance particularly influential.

The early 90s was a period of dominance for Ireland in the Contest - 1994 saw their third consecutive win, and they would win again in 1996. Traditionally the winner of the previous contest hosts the subsequent edition. Ireland, having hosted in an agricultural arena in rural Cork in 1993, wanted to put on something more spectacular in Dublin in 1994. The event was hosted at the Point, the city's major indoor arena, which is at the edge of the docklands, an area that had suffered from urban decay and was undergoing a period of significant development and regeneration. Ireland itself was undergoing a period of economic development (later known as the Celtic Tiger). Having begun the 90s as a poor country by Western European standards, it closed the decade as one of the richest.

Riverdance used the Liffey, Dublin's main waterway, adjacent to the docklands, as a sort of metaphor for the city's development. It took its inspiration from Timedance, a performance at the 1981 contest, which Ireland also hosted. The scale of the show, and the self-confidence of Ireland in how it had presented this modernised version of its traditional national dance, caused quite a stir.

Eurovision is extremely culturally significant for European audiences (hundreds of millions of people saw the show), and, having won and hosted several times, Ireland was seen as musically and culturally influential. Despite (putting it mildly) sometime strained relations with its neighbour, the UK, Irish musicians and artists are well-received by British audiences. Indeed, UK coverage of the contest was traditionally hosted by Terry Wogan, an Irishman; its current host, Graham Norton, is also Irish. Irish performers therefore have a large, well-developed, arts market to sell into, and the cultural significance of Eurovision across Europe made it even bigger.

However, with Flatley, an American of Irish heritage, there was an even larger market to tap into. The United States loves its Irish heritage. The huge St Patrick's Day celebrations in New York and Chicago dwarf anything that happens in Dublin. Flatley was able to act as conduit to bring this seemingly authentic (Irish traditionalists would dispute this) Irish dance to a mainstream audience in his native country, while the significance of Eurovision in Europe meant that it was similarly successful there.

So, three main things. Ireland was undergoing an economic and cultural boom, and was determinded to put on a spectacular show. The cultural importance of Eurovision meant that the show was widely viewed. And the show's lead performer was an American who could sell it well in the United States, making it a genuinely global phenomenon.