A 5.1 surround sound system uses 6 channels (feeding into 6 speakers) to create surround sound. 7.1 surround sound systems use 8 channels. The two extra channels of sound (and two extra speakers) provide a slightly better audio quality.
5.1 surround sound has 6 sound channels, and so 6 speakers. It includes a center speaker, subwoofer (for low frequency effects, such as explosions), left and right front speakers and left and right rear speakers. As it has a smaller number of speakers and is the industry standard, it is simpler to set up, cheaper and suitable for small or medium-sized rooms.
7.1 surround sound has 8 sound channels. It uses the same 6 speakers as above, plus an extra two side speakers. The extra two speakers add more depth to the surround sound experience. As it uses more speakers, 7.1 surround sound is more expensive and is only suitable for large rooms.
edit Supported Devices
Most Blu-ray players support 7.1 sound, as does the PS3. Most DVDs, Blu-ray disks and games are still produced using only 5.1 audio, but an increasing number of Blu-ray disks are being released with 7.1 sound as well.
5.1 surround sound was developed by Dolby Labs in 1976, and was first used for a theatrical release in 1992 for Batman Returns.
The first theatrical release to use 7.1 surround sound was Toy Story 3 in 2010. Disney intends to use 7.1 surround sound for all future 3D releases.
edit Related Videos
The following video talks about the pros and cons of 7.1 vs 5.1 surround sound home theater systems:
Prices for 7.1 surround sound systems are almost always higher than a 5.1 surround sound system from the same manufacturer in the same class. But there is a wide variation in prices charged by different manufacturers. 5.1 surround sound systems similarly range from $80 for a set of Logitech speakers to $1,700 for a KEF T305 home theater system. Prices for 7.1 surround sound speakers range anywhere from $265 for an Onkyo to thousands of dollars.
You can find the current price and other 7.1/5.1 products on Amazon: