"Welcum ta Meryod! We're all family heer!"
—Meryod citizen, Lunar: The Silver Star
Incest is a romantic or sexual relationship between close blood relations, which is taboo in most, if not all, societies -- primarily because it leads to birth defects. Or because it counts as abuse of power, where an older, trusted member of the family uses his/her status to get sex from another family member.
But this taboo is precisely is what is so exciting to writers, as incest creates an instant conflict between characters who would normally like each other, and a reason to have a really long Will They or Won't They? But it's also exciting to writers for other reasons. Writing is a way to explore ideas without actually doing them (we hope!).
This page is the supertrope of the Incest Tropes. Look to see if it goes there before adding examples here.