Rage is a really intense anger. Some frustrated drivers let their emotions boil over into road rage when another car cuts them off, for example.
If you're full of rage, you're full of anger — powerful, extreme, sometimes even violent anger. Rage can also be a verb: you might rage against something you hate or as the poet Dylan Thomas pleaded, "Rage, rage against the dying of the light." Things that rage are out of control, like a raging, roaring fire or a wild storm. Another meaning involves the latest, greatest trend — you'd say it's "all the rage."