On a normal bicycle when you lean off the vertical axis, a compensation is made by turning the front wheel towards the "inside" of the lean thus bringing the bicycle again closer to the vertical. i.e. the bicycle (with the help of your steering input) turns the front wheel to catch your fall. If you lean without steering you will simply fall over to the side immediately! Don't try to do this by the way =)

This is the same principle of balancing an upright broom vertically, handle first, on the palm of your hand. When the broom falls out of balance, you simply move your hand in the same direction to recover the center of balance. A bicycle is balanced by exactly the same principle.

Edit: Relevant Video: https://www.youtube.com/watch?v=2Y4mbT3ozcA