Originally "filk music" was a typo for folk music in a never-published essay on the influence of Science Fiction and Fantasy on folk music. Its first known deliberate use was by Karen Kruse Anderson in Die Zeitschrift fur Vollstandigen Unsinn (The Journal for Utter Nonsense) #774 (June 1953), for a song written by the well known science fiction author Poul Anderson.
Fandom being what it was (and is), the term was adopted for the songs, and musical parodies enjoyed by SF conventioneers. Practitioners are known as filkers.
The phrase 'science fiction themed parody folk music' fails to capture the full range of filk music, not least because it stretches all the way from writing "funny" (or very deep) words to established or original melodies, through writing new (and witty) words to a tune another filker has created, to all-out Filk Opera - Gilbert and Sullivan have been filked a few times, as has Cats.
However, the word "filk" has also been applied to music with an original score written about a science fiction or fantasy theme.
Filk can even tell an original story such as the "Before the Dawn" song cycle.
Filk is still sung in late night filk circles at Science Fiction conventions but there are also dedicated Filk conventions each year in the US, Canada, UK and Germany.