God-Emperor (and God-Empress for women) is a title used to describe a person in the unusual position of being both a god and an Emperor (or at least who thinks he is both). These individuals are usually tremendously powerful (politically and sometimes magically) and answerable to nobody, with the possible exception of other gods, which means that they are generally not nice people. In the real world, this title has been applied to the rulers of China, Japan, and Egypt, among others.
Arguably the most famous God-Emperors in fiction are Paul and Leto II Atreides.
Technically, the God-Emperor of The Empire is Sigmar, the deific personification of the first Emperor. During The End Times he returns in the body of Karl Franz and tries to defeat Chaos in the last battle for The Warhammer.
The most famous God-Emperor among /tg/-related pursuits is the God-Emperor of Mankind, from Warhammer 40,000, ruler of the Imperium of Man and the most powerful psyker in the galaxy. He wasn't happy about the "God-" part (even though he was certainly powerful enough to live up to the appellation), to the point that worshiping him as such was forbidden with extreme prejudice (just ask Lorgar), but after he mostly-died in the Horus Heresy, he was in no position to object.