Mirrors have two types: plane and spherical. Plane mirrors have flat surfaces and reflect an identical image. Spherical mirrors have a curved reflecting surface, either inward (concave) or outward (convex).
Makeup mirrors are concave mirrors. Their reflecting surface is curved inward, converging light to one point. They are also called converging mirrors. Your reflected image may be smaller, same size, or magnified depending on your distance from the mirror.
Concave mirrors are used as makeup mirrors because they show an enlarged image of your face when kept near, making it easy to apply makeup with intricate details. Check out Mirrorvana's makeup mirrors on Amazon.