From BlenderWiki

Copy Rotation Constraint

The Copy Rotation constraint forces its owner to match the rotation of its target.

Options

• Targets: This constraint uses one target, and is not functional (red state) when it has none.
• CSpace: This constraint allows you to chose in which space evaluate its owner’s and target’s transform properties.

X, Y, Z, -

These buttons control which axes are constrained – by default, the three ones are. The- buttons invert their respective rotation value.

Offset

When enabled, this control allows the owner to be rotated (using its current transform properties), relatively to its target’s orientation.

Examples

Objects:

Copy Rotation between objects example.

No constraint.

Owner copying rotation of Target_1, without offset.

Owner copying rotation of Target_1, with offset.

A Copy Rotation constraint applied to Owner empty, using Target_1 empty as target. In the third picture, the Offset option is enabled, and hence the owner’s rotation is offset from its target’s one.

Without the Offset option, the constrained object cannot rotate, it is stuck to its target’s rotation. With the Offset option, it can rotate, relatively to its target’s orientation…

Copy Rotation between bones example.

Target Space: World Space.

Target Space: Local Space.

Armature’s Bones:

The green constrained bone copies the rotation of the blue target one, using two different spaces to evaluate the target’s location. On the second picture, the “left” of the owner is not the same as the “left” of its target…

Here is one good use of the rotation constraint and local space. By setting the Influence value to 0.5, the small owner (green) bone will rotate half as far as its target (the blue bone). This is useful for character joints.