It means "proceed" but can have other meanings in particular contexts. For example, there is a famous line from an American movie, "Go ahead, make my day!" In this context, "go ahead" still means "proceed" but not in the sense of giving someone permission. Rather it means "proceed if you dare" or "proceed if you must."
Sometimes native speakers will also say "go right ahead." Example: "I want to start eating my dinner, the food is getting cold." "Go right ahead."