This is perhaps my favourite of the genres reading (and writing) fanfiction introduced me to, and while it is in spirit certainly not restricted to only fanfiction, it is it seems most clearly indulged there.
Hurt/Comfort is an easily-defined and yet very malleable genre. In its simplest form it is in just two parts, though those parts may be more complex in themselves.
One’s main character (or characters) suffer some manner of pain, be it physical (perhaps an accident or act of malice that leaves injuries) or mental/emotional (the loss of a friend, the failure of a quest, a break up); then that hurt is . . . comforted by another character or characters. How that comfort is provided – and whether it is a true ‘fix’ or merely soothing offered on the topic of something that cannot be simply repaired – depends on the situation and the writer, of course.
The idea is to break you character apart – to varying degrees, and this can be taken so far as to leave a reader teary-eyed and wondering if they are beyond repair – and then ever-so-gently restore them, piecing the broken shards into one cohesive whole and leaving a reader feeling relieved or delighted. Ideally, one should be wrapped up to some degree in the pain of the breaking and the happiness of the re-assembly. (Shouldn’t we always, ideally, be wrapped up by and drawn into a story, though?)
There’s a feeling of . . . satisfaction, to reading a well-done hurt/comfort story, in my experience. It might bring me out to the precipice and leave me dangling with my hand clutched over my heart for a while, but eventually it will bring me back to safe ground and assure me that everything is okay, probably even better now than it ever was before.