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.
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 and foreign country, but there is a subtle difference in meaning: to emigrate is to leave your country; to immigrate is to come into a new country.