In the United States, the states that touch the Atlantic Ocean on the eastern side of the country are called the East Coast. There are about 14 states on the East Coast. People contrast the East Coast with other parts of the country, like the West Coast or the Midwest.
A: Did you grow up here?
B: No, I'm from the East Coast.
Other countries can also have an east coast, if there's an ocean or sea on the eastern side. In some places like the U.S. and Australia, "East Coast" is capitalized. In other places, it isn't.