EP is short for "extended play". That means it's longer than a single (shorter than 10 minutes) but shorter than an album (longer than 30 minutes). EPs usually also have a title, as opposed to singles which are named after the first track. It isn't quite as simple as that, however. A recording longer than 30 minutes may be considered an EP, if only alternative versions of songs, remixes or anything like that is the only thing making it over 30 minutes long. And nowadays it's more about that the artist decides that it's an EP, and I recall at least one EP with less than 10 minutes of material. This also excludes singles with a bunch of remixes from being EPs.
EPs are often, but not always, a piece of their own, especially after the disappearance of the mini-LP due to the CD-age. This means that you might not find any of the EP's tracks on albums, like you would with a single. A famous example is Nine Inch Nails' Broken* EP, which is as considered as important as a full album in their discography. EPs were especially important to punk and other independant DIY-genres. Punk (especially hardcore) songs, as you might know, are quite quick, and you have to have more of them than "normal" songs in order to fill an album. And not only were EPs therefore easier to fill, but also cheaper to manufacture.
* Broken actually clocks in just over thirty minutes, but ten of those are two hidden tracks which are at a long distance (both by silence and their content) of the other tracks.