Stands for "original character." A character created by a fanfic
author or roleplayer. Said created character does not belong to the canon
cast but is inserted anyway for entertainment.
Many OCs appear as long-lost family members, past lovers, or exchange students. These background stories provide alibis for the sudden appearance and previous absences of the OC.
OC may also stand for "other character," in this case representing an extremely minor character, introduced or mentioned but not extremely active in an original series.
I was reading a person's fanfic the other day. It was centric of their OC, but the original character they made up was pretty cool, so I didn't mind.
Ayame is an "other character" from Naruto.