An assault weapon would be a weapon designed with the sole purpose of hurting a person. For example, a police/military grade AR-15 would be an assault weapon, but an AR-15 designed for hunting wouldn't. And since the title isn't specific, this wouldn't just apply to guns. Combat knives would be classified as assault, but a kitchen knife wouldn't.
I personally couldn't give two stuffs about what an assault weapon is politically. All forms of government can go to hell.