Multi-room systems are usually based around some kind of hard disk music server. This box digitally stores all of your favorite tunes, and then uses Ethernet or Wi-Fi connections to push that music around to the other rooms in your home. The advantages of this are huge, you no longer have to spend hours trying to find exactly the CD you want, or run around tuning every stereo in the house into the same radio station. Better still, different members of your household can listen to their own favorite tracks using individual room-based keypads/adapters, amplifiers and speakers, or listen to playlists that you've created. It's a great solution for parties and events.
The simplest multi-room or multizone system consists of a Speaker A/B switch that's probably built into your stereo or home theater receiver. Install speaker wires between the receiver's Speaker B terminals and two additional speakers in another room and you have a multizone audio system. It is also possible to connect the receiver to more speakers if you install a speaker switcher with a selector for each room. Multi-zone means multiple rooms and multi-source means the ability to listen to different sources in different rooms simultaneously.
If you own a newer multichannel home theater receiver you may be able to take advantage of its built-in multizone/multi-source features. Many receivers have multiroom outputs that can provide two-channel audio (and sometimes video) to as many as three separate zones. In some models, the audio output is speaker level so all that's necessary is speaker wire and two speakers in each of the rooms; or the audio output is line level (unamplified signals), which will require line level cables between rooms plus an amplifier and two speakers.
If you are fortunate enough to own a home with network wiring already installed, you've already got a huge advantage. The same type of wiring used to interconnect a computer network system can distribute audio signals to multiple zones. If you don't have a pre-wired home and retrofit wiring is too much to consider, there is another solution - go wireless. As wireless technology has improved, so have the options for wireless distribution of music. The most common wireless technology is Wi-Fi (Wireless Fidelity). No doubt you have heard the term used for the wireless networking of computers. The same technology is now finding its way into home audio.