An emigrant is a person who leaves his or her home country to live permanently in another country. Many Irish emigrants came to the United States in the late 1800s.
The Latin root of emigrant is emigrationem, which means "removal from a place." Don't confuse emigrant with immigrant, which tells about the person's status in the new country. When you leave your native land, you are an emigrant, and when you are already settled in a new country, you are an immigrant. It's a subtle difference, but with an emigrant, the focus is more on the home country.