(adjective)
relating to a person's background in terms of their race, culture, or birth as opposed to the country in which they currently live;
e.g. Many members of his family are ethnic Italians who moved to this country years ago.
(adjective)
belonging to or otherwise relating to a cultural group that forms a minority in a population/society, especially a non-Western group;
e.g. Each of these restaurants serves a different authentic ethnic cuisine.
(noun)
(dated, American, often offensive) a person who belongs to a cultural minority, especially when they retain their tradition's language, views, and customs;
e.g. She grew up in a rural town and had never met an ethnic before moving to the big city.