It is the direction in which the ball rotates forward. Cocking your hand in creates more rotation. Low axis rotation and early hook is in the 0 to 30 degree range, mid rotation is 40 to 60 and high rotation that creates length is 70 to 90 degrees.
When you are using an axis rotation you should make sure that you are centering the ball towards the edge in order for the axis rotation to take place without missing your mark.
Axis rotation will affect how the bowling ball rolls on the lane. When throwing the ball, if your axis rotation is rotating at a certain angle, then you will see that the curve is going a certain way.