What it means by 5.1 or 7.1 in a home theater system?

With respect to soundtracks, such as those on movies and DVDs, 5.1 means that the soundtracks are recorded with five main channels: left, center, right, left surround, and right surround, plus a low-frequency effects (LFE) bass channel (called a ".1" channel because it covers only a fraction of the frequency range of the main channels).

Some movie soundtracks use a variation on 5.1 called Dolby Digital Surround EX, which has now migrated via DVDs to home theater. This format matrix encodes a third surround channel onto the left and right surround channels of 5.1 soundtracks, and may be decoded or not at the cinema’s or home listener’s option due to their inherent compatibility. Because the extra surround information is carried on the left and right surround channels, Dolby Digital Surround EX encoded soundtracks are still regarded as 5.1 soundtracks.

With respect to home playback, the terms 5.1, 6.1, and 7.1 mean that there are five, six, or seven main speakers, plus a subwoofer, in the playback system. (The subwoofer reproduces the LFE channel recorded on 5.1 soundtracks, plus any bass the main speakers cannot handle.) The difference is in the number of surround speakers: two in a 5.1 system, three in a 6.1 system, and four in a 7.1 system.

Obviously, a 5.1-channel soundtrack can be played on a 5.1-speaker system. But it is not always understood is that it can also be played on a 6.1- or a 7.1-speaker system. To do this, the two surround signals on the 5.1 soundtrack are spread across the three or four surround speakers. This distribution can be accomplished by a Dolby Digital EX decoder, a THX Surround EX decoder, or other proprietary methods provided in home theater equipment by various manufacturers.