5.1/6.1/7.1 Channel Surround Sound
Surround sound uses multiple speakers to involve you in the action. "5.1 channels" refers to the use of 6 speakers: one centre speaker for dialogue, two front stereo speakers for effects, two rear surround speakers for ambient sounds and a subwoofer (that's the ".1") to increase the bass. 6.1 channel sound adds a rear speaker, and 7.1 adds two rears.
5.1 Channel Surround Sound
5.1 channels (2 front, 2 surround, a center and subwoofer) is the current standard for home cinema. The subwoofer is not strictly necessary if you have very large speakers to handle the bass found in movie soundtracks, but if you have limited space, the sub is one large box instead of five large boxes. There is also usually unique sonic information encoded in the surround sound track especially for the subwoofer, so without one you might actually be missing out on some effects.

6.1 Channel Surround Sound
Some more expensive surround sound amplifiers extrapolate an extra channel to fill in the space between the surround speakers. This rear channel can be represented by either one or two speakers behind the listening position. Soundtracks do not include an actual discrete channel for this rear channel, so some users don't see the worth of adding an extra speaker and cabling.

7.1 Channel Surround Sound
On the far end of the home theatre speaker count is the 7.1 speaker set-up. The surround amplifier extrapolates two rear channels for maximum coverage. There's no sonic disdvantage to this many channels, but the drawbacks are that you'll have less to spend per channel (meaning lower quality per channel for a given budget) and you will need to share your lounge with even more speakers and more cables.

And Beyond...
Some top-of-the-range equipment includes 2 subwoofer channels (referred to as "x.2" surround) to add even more power and control to the bass, and the very latest amplifiers add two "Z" channels above the front speakers to allow the surround to move in the vertical plane. There is really no commercially available software out there that fully takes advantage of these developments, so they can be considered novelty features. The rule of thumb for sound quality is to spend more on less.
For more information, return to the HDTV glossary introduction.