Anyone who has fired a gun knows that when you shoot, the gun kicks back. This kickback is caused by the conservation of momentum. Before the gun is fired, the bullet and gun have a combined zero momentum. When the gun is fired, the bullet gains a large momentum forward. In order for momentum to be conserved, the gun gains an equal momentum backward. Since the bullet is so much less massive than the gun, the bullet goes much faster than the gun—the more massive a gun is, the smaller the kick back will be. Often, a person puts the end of a rifle they are firing firmly against their shoulder. This is effectively adding their mass to the mass of the rifle, and the kick back velocity becomes much smaller.

A rocket works by the principle of conservation of momentum. A rocket sitting on the launch pad has zero momentum. When the rocket engines ignite, hot gasses come shooting out one end of the rocket at an incredibly high velocity. This gas has momentum down. In order for momentum to be conserved, the rest of the system (the rocket) has to gain an equal momentum up.

Source: Rocket cart, Rick Matthews, Wake Forest University