In a literal sense, it means he lost control of his urethral sphincter, thus causing an involuntary urination in his trousers or over himself. As Neal states though, this expression is not always used literally.

It could be either, depending on context. Usually, however, it will either be 'he peed' (especially if it's a baby), or a part of the idiomatic expression 'he wet himself laughing', which means he was laughing so much that he lost control of his bodily functions! The person does not actually have to pee for you to use be able to use this expression about them; it just signifies that he found something extremely funny and could hardly stop laughing !!