Emigrate means to leave one country or region to settle in another. Example: In 1900, my grandfather emigrated from Italy.
Immigrate means to enter another country and reside there. Example: Many Mexicans immigrate to the U.S. to find work.
**The following hint may help you remember the difference:
Emigrate begins with the letter E, as does Exit. When you emigrate, you exit a country. Immigrate begins with the letter I, as does In. When you immigrate, you go into a country