If you move to a different country, you emigrate. For example, if you are Canadian and you emigrate to Italy, you aren't on vacation — you are making Italy your new home. Benvenuti!
The verb emigrate comes from the Latin word emigrare, which means “move away,” or “depart from a place.” The words emigrate and immigrate both mean that a person has decided to permanently live in a foreign country, but to emigrate is to leave your country, and to immigrate is to come into a new country. To emigrate is to exit.