Non-con, short for non-consensual, is a term used in fanfic to describe a situation in the fic where at least one character is forcing another character (or several of them) to participate in an act that the second party Does Not Want to do.
This is usually used for smutfic, and the non-con is very often synonymous with rape.
Depending on the canon and characters involved, non-con can be a charge. This does not stop the fandom, however.