A cup is a vessel used for drinking. Your grandmother might make it a habit never to go to bed without a cup of warm milk.
A cup is like a small bowl with a handle. It's also a unit of measurement in cooking — if a recipe calls for a cup of water, it's the same as eight ounces. If you cup your hands, you form them into a cup shape, which you do when you hold a baby bird or cup your hand to whisper to your friend. If you say, "Polka music's not my cup of tea," it means you don't love it.