I'll be assuming that when you push your back foot out, the board pivots about the point directly between the front wheels. In that case, in order to begin the skid you need to apply a torque to the board using your back foot. If your back foot is a distance $r$ from the front wheels, then the torque will be
$$
\tau = r \times F
$$
Where $F$ is the force applied by your foot parallel to the ground. You see that if your back foot is further back (which is possible for longer boards) then a greater torque will be produced by the same amount of force. This is why it seems easier to do this type of carving on a longer board.
As for why this is effective for breaking, that's because while the wheels are rolling you are only having to deal with the friction between the wheels and the axels, which the board has been designed to minimize. However, when you begin to skid, the wheel are no longer rolling, but sliding across the pavement. This has the same effect as locking the wheels on a car.