A wedge is used to track objects. When you plan to take sharp photographs with long shutter times a wedge is indispensable. This is because a wedge counters the effects of field rotation. When you look up to the sky at night, you will see celestial bodies slowly arcing from the East to the West. The wedge enables you to polar align the rotation axis of the telescope with the rotation axis of the earth; this eliminates the effects of field rotation and reduces image smear.
The most frequently used wedge is the parallactic wedge (also known as equatorial wedge). This wedge is placed between the tripod and the mount.
The wedge looks like a U-shaped mounting bracket. You use this bracket to mount the telescope on the axis of the tripod. Just move the wedge from left to right: you will see your telescope slowly moving across the horizon in a nice curve.