What is the difference between words immigrate and emmigrate?

You've got it almost right! It's immigrate and emigrate. Here's the difference:

* Emigrate: To leave one's own country to live in another. (Think "exit" for emigrate)

* Immigrate: To enter another country to live there permanently. (Think "into" for immigrate)

Example:

* Emigrated: "My grandparents emigrated from Italy to the United States."

* Immigrated: "My parents immigrated to Canada from India."

In a nutshell: Emigrate is about leaving, while immigrate is about arriving.