The forward slip changes the heading of the aircraft away from the down wing, while retaining the original track (flight path over the ground) of the aircraft.
To execute a forward slip, the pilot banks into the wind and applies opposing rudder (e.g. Right aileron + Left rudder) in order to keep moving towards the target. If you were the target you would see the plane's nose off to one side, a wing off to the other side and tilted down toward you. The pilot must make sure that the plane's nose is low enough to keep airspeed up. However, Airframe speed limits such as VA and VFE must be observed.
A forward-slip is useful when a pilot has set up for a landing approach with excessive height or must descend steeply beyond a tree line to touchdown near the runway threshold. Assuming that the plane is properly lined up for the runway, the forward slip will allow the aircraft track to be maintained while steepening the descent without adding excessive airspeed. Since the heading is not aligned with the runway, forward-slip must be removed before touchdown to avoid excessive side loading on the landing gear, and if a cross wind is present an appropriate sideslip may be necessary at touchdown as described below.
In the United States, student pilots are required to know how to do forward slips before embarking on their first solo flight. The logic is that in the event of an engine failure, the pilot will have to land on the first attempt and will not have a chance to go around if the aircraft is too high or too fast.