A person's ethnicity is their ethnic traits, classification, or association. If your ethnicity is Italian, you might speak Italian in the home and eat Italian food. Or you might simply refer to yourself as Italian and identify with your ethnicity in no other way.
Usually, ethnicity is a collective noun, but in the singular, an ethnicity is a particular ethnic group. The adjective ethnic relates to large groups of people who have certain racial, cultural, religious, or other traits in common. In Middle English, ethnic meant heathen or pagan. The word is from Late Latin ethnicus, from Greek ethnikos "foreign," from ethnos "nation."