Migrate: for humans and animals. It conveys the seasonal or periodical movement. It signifies the actual action of movement from a place to another.
Emigrate: The prefix e- (or ex-) usually means "out of" or "from."
Immigrate: The prefix im- (or in-) often means "in" or "into."
If I migrate from Germany to France, I would emigrate from the point of view of Germany and immigrate from the point of view of France
Therefore, emigrate means "to move out of" and immigrate means "to move into."