There are many types of bridges each of which serves it own purpose. However, the main function of the bridge is to lock your cue stick into position to minimize unnecessary sideways movement.
The closed bridge (see below) is widely used by many players. Because of the way the cue stick is wrapped around by your fingers, this type of bridge has a few advantages over the open bridge. First, it prevents unnecessary sideways movement of your cue stick thus preventing miscues. It is also better for power shots where you draw your cue as far back as possible. Using a closed bridge allows more control over the movement of your cue stick.

The open bridge (see below) is widely used by newer players mostly because it easier to set your hand for an open bridge than a closed bridge. This type of bridge is useful for soft shots and follow shots.
