What physical phenomenon causes racing bike to lift automatically after it fall down?

In all motorcycle front steering layouts, there is a characteristic called trail which is an offset between the point where the front tire touches the ground and where a straight line drawn down through the fork pivot hinge meets the ground. because the tire's contact point is behind the fork pivot line's touchdown point, a motorcycle will by itself tend to turn into the direction of a lean, which makes the motorcycle try to right itself and not fall over. the greater the amount of trail, the stronger this tendency is.

In addition, when the bike goes into a sideways skid, the roadway applies a friction force which opposes the skid direction while the bike's momentum urges it in the forward direction. this sets up a torque which usually causes the bike to flip and begin tumbling down the road, but if it is not too great then it will also tend to "unlean" the bike and urge it upright again.

I suggest you search on youtube for motorcycle crash videos posted by rnickymouse, they are shot in hi-def and slo motion and reveal a lot of interesting motorcycle dynamics like this.