Mental event is a sort of catch-all phrase that means a particular occurrence of something going on in the mind. So say Mary is walking through a park and she sees City Hall. That instance of seeing City Hall is an instance of perception -- something that is supposed to be going on in Mary's mind. That instance of seeing is a mental event. It’s an event because it is something that happens; and it’s mental because it happens in someone's mind. If Mary thinks to herself, "I am a human being," that thought is a mental event; if she feels happy after doing well on an exam, that’s a mental event. And so on.
See also: quale