Why does the stagnation point on airfoil move with the angle of attack?
At the stagnation point, the streamline is directly perpendicular to the airfoil. As angle of attack increases,  the streamline is no longer perpendicular to the leading edge (which is where the stagnation point is usually located at 0 angle of attack). This is the best explanation I can come up with for why the front stagnation point moves as it does.
The rear stagnation point is usually located at the trailing edge of the airfoil, thanks to the Kutta Condition which says that, "A body with a sharp trailing edge which is moving through a fluid will create about itself a circulation of sufficient strength to hold the rear stagnation point at the trailing edge." (according to wikipedia). The airflow around the airfoil, which is a body with a sharp trailing edge, keeps the rear stagnation point where it is. 
This moving of the front stagnation point as the AoA increases is part of the reason why lift increases with increases in AoA.