A mug is a large deep cup with straight sides and a handle, used for hot drinks.

If someone mugs you, they attack you in order to steal your money.

If you say that someone is a mug, you mean that they are stupid and easily deceived by other people.

If you say that an activity is a mug's game, you mean that it is not worth doing because it does not give the person who is doing it any benefit or satisfaction.

Some-one's mug is their face.