Crabbing is basically cross-controlling the airplane (i.e. using the aileron or rudder or both in opposition to each other).
For example, on an approach, aligned with the center line, a crosswind is pushing your flight path away from the centerline. You can use a small amount of rudder in the direction the wind is coming from to keep the flight path aligned with the runway while the nose is pointed away from the centerline enough to correct for the wind drift.
Crabbing with both rudder and aileron is often used during a descent to landing when the pilot finds him/her self significantly too high when nearing the touchdown point. It is also called a "slip" when used for this purpose. It allows the airplane to lose altitude at a higher than normal rate without also increasing air or ground speed.
From the pilots perspective, the wing in the direction of the turn is banked toward the ground while the nose is pointing away from the runway in the opposite direction. Done correctly, the flight path stays aligned with the center line of the runway and the pilot straightens the nose and lifts the wing to level just prior to touchdown (or earlier if he/she has lost the extra altitude before touching down).