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A songfic, also known as a song fic or a song-fic, is a work of fiction interspersed with the lyrics of a relevant song. The term is a portmanteau of "song" and "fiction"; as such, one might also see the genre referred to as "songfiction". Songfics are a genre of artwork related to fanfiction in that both involve the poaching of text. The interplay of commercial art and folk art make songfics also similar in some ways to filk music, much of which uses commercial science fiction or fantasy as inspiration.
Comparison to parodies 
Parodies, by definition, contain rewritten lyrics to a well-known song; this is usually, but not always, meant to be humorous. "Weird Al" Yankovic has made a career out of humorous parody.
By contrast, songfics leave the lyrics of the source song alone; the song's lyrics are incorporated into a more-or-less separate story. It is similar in concept to a music video, where the music and the story are designed to complement each other. As a general rule, instrumental songs cannot easily be incorporated into songfics, due to the lack of lyrics to go by.
As many lyrics are under copyright, whether songfics are a violation of that copyright law is a relevant topic. FanFiction.Net has barred authors from posting songfics with lyrics outside public domain.