Originally Posted by Robstar
Multicamera shows (HIMYM, Two and a Half Men, Friends etc.) film the action with multiple cameras at a time. You'll see on HIMYM how you only ever see three walls of the apartment, that's because the set is open ended and the scenes are usually filmed in one whole shot with multiple cameras.
Single camera shows (Community, Cougar Town, Arrested Development) film the action one camera at a time.
Multicamera shows are simpler and cheaper to produce, and are usually filmed in front of a live studio audience to get the background laughter you hear when watching the shows, but single camera shows can experiment more with the film-making (for example, Community does a lot of things that probably wouldn't be possible with multicamera styled filming.)
Hope I've explained it ok, I'm pretty awful at explaining what things mean.