A rocket is a space vehicle or missile, or the special engine that's meant to propel such a vehicle into the air. You can even get a model rocket that's small enough to shoot off in your back yard.
A rocket or rocket engine uses thrust to propel something toward the sky, whether it's a spacecraft that will orbit the Earth or a bottle rocket that will explode overheard. You can use the word as a verb, too, to mean "move rapidly": "Without a parachute, the skydiver would rocket to the ground." It also means "increase rapidly": "After the election, the price of gas began to rocket upwards."