This constraint copies the rotation of the target. As simple as that. It can be an object or a bone. As you can see in the example, only the rotation gets copied.
The Constraint PanelEdit
Where To Use ItEdit
Can be used with Copy Location to fake parent relationship. As you can key the influence you can make a character pick something up and hold it in his hands. Check the .blend for the hand-glass scene.
(?)link to the Blend(?)
You can also use this to align a plane with a 2D effect on it to the camera at all times. This works better than pointing it at the camera in some cases, such as a ring of atmospheric halo around a planet, where you don't want it disappear behind the planet.