To be enraged is to be full of anger. Enraged people are in a fury.
Rage is anger, and when you're enraged, you are extremely angry. When you're enraged, your face might turn red and you might hurl obscenities or throw a fit. This is a strong word: getting enraged is a lot more serious than getting annoyed. An enraged person is out of control. Some people are more prone to getting enraged than others.