The angular momentum of a rotating wheel points along the axis of rotation.
Torque is a vector
A tangential push on the spinning wheel produces a torque which causes the angular momentum to increase
Gravity produces a torque which is perpendicular to the angular momentum
The change in angular momentum causes the gyroscope to precess
A bicycle wheel is hanging from a rope on one end of its axle, as shown. A person is holding the other side of the axle. What happens to the wheel when the person lets go? How about now?