The horn is a brass instrument that consists of tubing wrapped into a coiled form, now with finger-operated valves to help control the pitch but originally without valves to control the pitch.
The instrument was first developed in England as a hunting horn in about 1650. The French refer to the modern valved instrument as the horn of harmony, the Germans call it the hunting horn and the English and Americans call it the French horn. Most musicians usually refer to it simply as the horn.
The natural horn is the ancestor of the modern horn. Basically descended from hunting horns, it is controlled by mouthpiece tension, tuning crooks and the use of the right hand moving in and out of the bell pulling the pitch up and down.
Single horns use a single set of tubes connected to the valves. This allows for simplicity of use and a much lighter weight. They are limited to the keys of F or B-flat, depending on the tuning valve used. Despite the introduction of valves, the single F horn proved difficult for use in the highest range, where the partials grew closer and closer, making accuracy a great challenge. An early solution was simply to use a horn of higher pitch -- usually B-flat. The use of the F versus the B-flat horn was a hotbed of debate between horn players of the late 19th century, until the German horn maker Kruspe produced a prototype of the "double horn" in 1897.
The double horn combines two instruments into a single frame: the original horn in F, and a second, higher horn keyed in B-flat. By using a fourth valve (operated by the thumb), the horn player can quickly switch from the deep, warm tones of the F horn to the higher, brighter tones of the B-flat horn. The two sets of tones are commonly called "sides" of the horn.
The term 'horn' is also a popular term used to refer to a broader range of brass instruments.