I've cut and pasted the following from the web:

The definition of the word "filk" itself is somewhat nebulous. It is easier, however, to pinpoint the origin of the term "filk". According to several sources, the term came from a typo. In her essay on the history of filking (see references at the end of this article), Lee Gold points out that the typo was made by a fan submitting an essay to SAPS (Spectator Amateur Press Society). In his title, ""The Influence of Science Fiction on Modern American Filk Music", the word "Filk" was originally supposed to be "Folk". The essay was rejected, but word spread about the typo, and the term stuck.

By the way the first time I heard the term was from a fantastic Harp player from thye states who visited folkmob several times a few years ago called Gwen Knighton.