A Fan character is a fanmade character for a fan fiction story, background to a fan class or a fan monster made by a fan of the Diablo franchise. There are many varieties of these characters; good or evil and beyond.
Background
A fan character is a character based on the Diablo universe, but not part of the official lore. These fan characters are not canon.
The characters can be from any setting, alternate reality, and so on, but still relates to the world of Diablo.
Some writers also use main characters from Diablo I, Diablo II and some from Diablo III in fan fiction stories as well, mixing in "real" characters and fan characters.