Nightmare is kind of like a secondary status, because it takes out 25% of your HP every turn. You can easily switch out to stop it. (hopefully nobody used mean look first.)
Dream Eater is like Giga Drain in that it saps your health, and the user gets some HP back. It has higher base power than Giga drain, but is harder to use, since the victim has to be asleep.
Both of them require the pokemon to be asleep obviously.