PODs are digital modeling and multieffects devices.
They are used to jam along with a pair of headphones with no need for an amp. They can also be used with an amp, as if they were a normal multi-effect unit.
Most can be used to record via USB
Some of them are built like pedal-boards, they are the "Live" models. They are suitable for gigging or when you need to change effects/models while playing.
There's a thorough review of a specific model of POD here: Pocketpod
And there's plenty of info at the manufacturers site, Line 6: Line-6 Site
(This article is so far just a small wiki so that anybody can find some information when searching for the word "POD".) Feel free to add some more info!