1. Being a (citizen) because you were born in the country.
Mr. and Mrs. Schmidt came to the United States from Germany and are naturalized citizens but their children are natural-born citizens.
2. Born with great ability to become (something); having great ability (as in a sport or art) almost from the start.
Joe had never played baseball before trying out for the team but he showed that he was a natural-born pitcher and he became the best in the league.
Mozart was a natural-born musician. He could play the piano well when he was only six years old.