Striking the cue ball below centre causes it to rotate backwards as it travels forwards. Cloth friction will convert this motion into a skid and eventually a roll. A drag shot occurs when the cue ball starts off rotating backwards but begins rolling before contacting the object ball. It is reasonably easy to see the point at which the skid turns to roll as the forward motion of the cue slows before this point and speeds up after it.
Advantages of Drag
The main advantage of drag is that shots can be played much faster than normal, limiting any roll-off that the table may have. Furthermore, if you play with side AND drag, you will get more side on the cue ball due to below centre striking and also the fact that you will strike the cue ball harder. As the cue ball will initially travel faster than a plain ball shot, the side will stay on the cue ball and be there when the drag finishes.
Most club players use drag effectively to prevent roll-off. A typical shot would be a loser, played from hand, with the object ball near the top cushion and close to the corner pocket.
More advanced players use drag on a huge variety of shots. One simple example is a Short Jenny. In this case the drag is used to retain the side on the cue ball; there is very little danger in the cue ball rolling off over a short distance, but the side is held on the cue ball by playing with drag. A more advanced shot would be the run through in-off. In this case it is essential that players can judge when the cue ball will be skidding or rolling; if it is still skidding as it contacts the object, ball a stun would occur!