Most paintball markers have the tank connection at the bottom rear of the gun. A dropforward attaches to that point, and drops the tank below the marker, and moves it forward so that it's roughly even with the rear of the gun. This makes the marker more compact, and allows you to hug your cover, as well as allowing for a better field of vision. If you're considering playing in a drop forward style, a paintball gun stock is essential.
A drop foward can be useful for a pump paintball player, because it cuts the distance from the player to their pump, and can be especially useful for players with shorter arms.