A man walks up to you and says:
"Everything I say to you is a lie.
Is he telling you the truth or is he lying?
The man says that everything he says is a lie. That "everything" he speaks about includes what he had just uttered. If the statement is a lie then everything the man says to you is not a lie (by contradicting his statement because it is a lie). So if what he says is not a lie then it must be a truth. But if it is a truth then his statement must also be true (That everything he says is a lie).