The name of a popular anime/manga character staring in a show of the same name. InuYasha, broken down, roughly translates to dog demon.
', meaning dog, and 'Yasha' being a slang/broken term of 'youkai' which means demon or other worldly (non human) creature. Often 'Yasha' is refered to mean half demon.
InuYasha is a half demon. His demon blood comes from his fathers side and his human blood comes from his mothers.