Horn is a hollow pointed projection of the skin (generally on the head). Its main component is the protein keratin.
Antlers are not horn, being bone, and shed annually, whereas horns are permanent structures.
Once separated from their animal, horns are capable of being used (by a process of softening and remoulding) for a variety of purposes -- including as knife handles, as cutlery, as lenses (in, for example, early spectacles), or as small semi-light-permeable windows.
Horns from bovid (cow-like) cretures have also long been adapted for use as musical instruments and as drinking vessels.
Note: The "horns" of the rhinocerous are actually made of compacted hair, not true horn.