Exception that proves the rule means that if something is usually true, but there is an example that shows it's not true, this example proves the rule. For example, let's say that rules of a school give an example that students must be in class every day. But if there is one special occasion where students don't have to be in class, like a holiday, then that special case proves that the rule is true, because it shows the rule can be broken on rare and special occasions.