Here is a link to the wikipedia entry for more info, but the quick answer is that, on the night of June 27-28, 1969, the police raided a known gay bar, the Stonewall Inn on Christopher St. in NYC. Rather than the usual running off, or going quietly in paddy wagons, the patrons fought back. It was 1am, it was hot, and people were drunk. Also, it was 1969, and a spirit of revolution was in the air. Objects were flung, the police and gay people faced off, notably a number of transexual patrons, then known as "street queens," or "drag queens." People had had enough, and it lasted the night. The next night a lot of gay people from around the city came to the Stonewall to protest, and face the cops again. This was seen as the beginning of the gay liberation movement. "The shot glass heard 'round the world," I've heard it called, which I think is excellent, and thought you'd appreciate.
But the really important thing happened on the anniversary, the next year. A commemorative march was organized, which has since become the Pride March or Pride Parade, and from there a movement really coalesced. So, this being the 50th Anniversary of those first nights of resistance in 1969, there's a big commemoration here in New York this weekend. This one is being called World Pride, and it's going to be massive.