well if the object is not deforming then you only need to parent it to the joints to animate it.. if it deforms you have to bind it in order to have control of how much influence each bone has over vertices in the mesh.
Constraints work sort of like parenting except you can control the rotation, translation and scale all separately with different objects and the constrained object does not have to live under the hierarchy of the controlling object. Constraints also have the advantage of allowing you to control and object with multiple "parents" or controllers and allows you to blend between their influence.
Rigging and binding is a pretty heavy topic.. you'll want to look for some some tutorials on the subject.. I believe there are a few online here in the tutorial section.