Curtain Fic is a term for stories that focus on a romantic domesticity – as in "they moved in together and started picking out curtains".
In Supernatural fic, these often focus on a time after Sam and Dean finish hunting and settle down together or on interludes when they stay in one place, often due to one brother being injured. The stories are predominately Wincest or Destiel. There are also versions of the stories which are Gen (usually featuring Sam and Dean as retired hunters) or even Sam and Dean settling down with a female partner. Stories with any pairing may also overlap with Kid Fic.
J2 stories in this genre have always been around, although when Jared and Jensen started sharing a house in Vancouver in mid-2008, the number of stories written in the genre increased markedly.