To complete the series 2.1 has 2 speakers and a sub.
5.1 has 5 speakers and a sub. 3 front speakers and 2 surround speakers at the sides of the room. The surround speakers don't have to match the front speakers but they should sound sonicly similar. It is best if the front speakers all match.
7.1 has 3 front speakers, and 4 surround speakers. 2 on the sides and 2 behind. Gamers prefer 7.1 sound because it gives them an advantage is locating enemies behind them.
There are also 10.2 and 14.2 systems. They are identical to 5.1 and 7.1 systems with the addition of high mounted speakers at all positions to give hight location cues, and stereo subwoofers. At this point in the game 10.2 and 14.2 systems are purely experimental.
To make a quantum leap in sound quality you have to double the number of speakers. So going from mono to stereo was a huge improvement. Going from 2 to 5 speakers (they added a center speaker so dialog sounds like it's coming from the screen) is an equally large improvement. And going to a 10.2 system has the potential to be another huge improvement.
If you want your movies to sound the way the director intended them to sound you need a 5.1 system. Almost all movies are now mixed in 5.1 sound. DVDs have these 5.1 sound tracks on them. There are very few movies with 7.1 sound because most movie theaters have 5.1 systems. But if you are a gamer you want 7.1 sound.