Mashups are 2 or more songs mixed together to sound like one song. Usually done by DJ’s with 2 unrelated songs. This article explains it in more detail.
I wouldn’t classify a remix of an old song, such as P. Diddy’s “I’ll Be Missing You” or Trick Daddy’s “Let’s Go,” neither of which could be classified as anything substantial. Mostly they just ruined good songs.
Some of the more memorable mashups:

• “Boulevard of Broken Songs” (Green Day and Oasis) – They’re playing this on 102.9 The Buzz here in Nashville. Since I like both songs, I think it sounds great together. The dark Green Day lyrics are complimented by the upbeat Wonderwall lyrics. Excellent song. Hear it here.
• The Beastles (The Beastie Boys and The Beatles) – The Beastie Boys are a bit grating at times. However there are some good points on this album. “What You Want, Lady?” (Mix of “What You Want” and Lady Madonna”) is one of the better songs on the album.