Paradox meaning of "Everything I say is a lie"?

The statement is paradoxical because it can not be true.

If everything that you said was really a lie, then you would not be able to say, "Everything I say is a lie," because that would be a true statement. Therefore it can never be truthfully said.

You could say, "everything that I say is a lie," and be lying, but that statement is still false at that point because you're lying while saying it, which means that you can tell the truth.