The spin angular momentumis along the rotation axis as shown, but the torque about the support point is in a direction perpendicular to the angular momentum. The torque produces a changein L which is perpendicular to L. Such a change causes a changein direction of L as shownbut not a change in its size. This circular motionis called precession.
If the wheel is not spinning, the apparatus just rotates downward toward a vertical orientation. If you curl the fingers of your right hand in the direction of that expected rotation, then your thumb will point perpendicular to the spin axis in the direction of the torque produced by gravity. The tip of the angular momentum vector, and therefore the axle of the wheel, will precess in that direction.