THE HORN, A SIMPLIFIED EXPLANATION
OK, so what is a horn and how does it work? Essentially, it's a waveguide in that it guides the soundwave from the source to the space at the end of the horn; here the source is the loudspeaker and the space is the listening area. It's also referred to as a transformer or to be more specific, an acoustical transformer. In the case of an electrical transformer, the input, usually a high voltage (low current) across a high resistance/impedance is transformed to a low voltage (high current) across a low resistance/impedance
Consider a brass instrument, such as a trumpet. It's a horn, plain and simple. Here, the loudspeaker is the players lips. If the player were to pucker his/her lips and blow into free space, one wouldn't hear a very loud sound. However, place the lips at the mouthpiece of the trumpet, (the throat of the horn) and the sound becomes very loud with the same effort exerted by the player. At the players lips there is a high resistance, or impedance to the flow of air followed immediately by a low resistance, or impedance in the surrounding area. The result is the sound wave spreads out very fast in all directions, called a hemispherical wavefront which tries to become spherical in that it will wrap around the player. It has nowhere to go but everywhere. The horn kinda points the direction.
If you've ever been to an outdoor rock concert you may have noticed the array of different shaped horns. The reason for the different shape is to focus the emerging soundwave to a particular area of the audience. In the photo below, this horn will cover a very wide area at the rear of the audience. It has a 120 degree horizontal dispersion and a 30 degree vertical dispersion. The rapid rate at which it expands governs it's low frequency limit, probably around 600 Hz.