Migrate, emigrate, immigrate are used of changing one's abode from one country or part of a country to another.
To migrate is to make such a move either once or repeatedly: to migrate from Ireland to the United States.
To emigrate is to leave a country, usually one's own (and take up residence in another): Each year many people emigrate from Europe.
To immigrate is to enter and settle in a country not one's own: There are many inducements to immigrate to South America.
Migrate is applied both to people or to animals that move from one region to another, esp. periodically; the other terms are generally applied to movements of people.