A filk is a song, usually a traditional or well-known one, for which the words have been re-written by fans for a specific fandom.
The word originated with a typo of "folk." According to filk fanzine Xenofilkia, "SF fans have been writing songs (sometimes parodies, sometimes to original music) since at least the 1940s, but they didn't start calling them 'filksongs' until the early 1950s. That was when Lee Jacobs mistyped 'folk' as 'filk' in a fanzine article on folk music. Karen Kruse (later Karen Anderson) liked the word and used it to describe the long-standing fannish phenomenon, and the use caught on."
Filks and filking should not be confused with songfic, which is an entirely different critter.
PPCers are responsible for a fair bit of filking. For example, see the PPC Holiday Songbook.