EP= Extended Play
LP= Long Playing record
An EP contains a few songs (usually around 3-5 songs), and an LP is a full album. The terms are from the days of vinyl records. In the 1980's, promotional vinyl EPs were often sent to clubs and radio stations to give an overview of an artist's music, and live EPs of top-selling artists were sometimes sent to radio stations to promote the artist on tour and extend the life of an album. The popularity of the promotional EP caused labels to start manufacturing them for the general public, often in colored vinyl and with previously unseen photos used as cover art.
As for the difference between an EP and a single, CD singles have blurred the meanings a bit, but originally a single contained 2 songs: one on the "A-side", and one on the "B-side." (During the days of vinyl singles, occasionally an extra song would be included, though not often.) CD technology allowed more minutes of music than previous music formats, so labels took advantage of it and added "bonus tracks" to some CD singles. Technically speaking, a CD single with bonus tracks is actually an EP...but labels found that calling it a "single with bonus tracks" made it more appealing to consumers.