Muffin cups, also called baking cups or cupcake liners, are small paper, foil, or silicone cups that line the wells of a muffin tin so batter can be baked and removed without sticking to the metal.
Paper liners are the most common and least expensive option; foil liners are sturdier and hold their shape better for delicate batters; silicone liners are reusable and nonstick, and can also be used freestanding on a baking sheet without a tin. Beyond muffins and cupcakes, the cups are used to portion and bake other single-serving items such as mini quiches, frittatas, and mini meatloaves.
Muffin cups are a convenience item, not a structural requirement: greasing the tin directly works as well for most batters, but liners make removal cleaner and let bakers portion batter more precisely.