The strict definition of rotation is the circular movement of an object about a point in space. This delineation of rotation can be applied to any object (whether it is in two dimensions or three or more), but in the realm of astronomy and cosmology, obviously three dimensional objects are of the immediate concern.
In this case, a three dimensional object will rotate about an axis - an imaginary line that the object moves around.
Rotation versus Spin
When the axis of rotation pass through the object it is said to spin.
Rotation versus Revolution versus Orbit
It is not necessary, however, for the axis of rotation to actually pass through the object in question. In some cases the axis of rotation is outside of the object all together.
In such cases the rotation is called revolution. Examples of revolution would be a ball on the end of a string, or a planet going around a star.
But in the case of planets orbiting stars, the motion is usually referred to as orbit.
The Earth-Sun System
In some systems there are multiple axes of rotation. One classic astronomy example is the Earth-Sun system. Both the Sun and the Earth rotate individually, but the Earth also rotations, or specifically orbits, around the Sun.