Horns were the original amplification device. Prior to amplifiers, horns were the only choice for early sound engineers. The exponential design of a horn mimics the human ear - in reverse! The human ear captures sound via a large aperture (the outer ear structure) and funnels it via a narrowing tube (the ear canal) to the ear drum. Small bones in the ear connect to the drum and mechanically transmit the sound vibrations to the inner ear nerve bundles (the cochlea) which then send their signals to the brain for interpretation as sound.
In the early audio devices: gramophones, radios and speakers the lack of powerful amplifiers mandated the use of horns. There was no other way to get sound levels up to listenable levels. Now we don't really know what prompted the early engineers to use horns but I suspect that they developed them from the way the human ear works. In this case however the needle of the gramophone picks up the groove vibrations, which is mounted to a diaphragm which sends vibrations as sound waves into an expanding tube. That tube then connects to a large exponential horn ( loudspeaker element which uses an acoustic horn to increase the overall efficiency of the driving element) which amplifies the sound many fold. You then can increase the volume of the small acoustic signals to be audible enough for room filling sound.
This same concept is employed for most, if not all professional sound stages, live concerts, and very expensive home entertainment systems such as the Avante Garde speaker (image courtesy of: Christian Herzog) - costing upwards of $30,000 USD. Why do they employ these expensive systems when there are much less expensive options? Several valid reasons: for home audio - Horn loudspeakers can provide very high efficiencies, and they are a good match for low-powered amplifiers such as triode amps or other tube amplifiers. They also focus the sound stage, via controlled dispersion which pinpoints sound images and avoids messy reflections that plague conventional speakers. Horns can produce up to 3 times the sound volume per watt than conventional drivers. Horns also provide less driver interactions via their focusing of the sound waves. When speakers use multiple drivers, those drivers interact with each other in negative ways causing peaks and valleys in the sound they produce. Moving your head or seating position makes these distortions worse.
The graph below shows distortion in our Super Hiro speaker at 1 meter.
When distortion reaches 1% it is just 40 dB lower than the music. When distortion reaches 0.1% it is 60 dB lower than the music.
How about that old description of horns sounding "shouty" or that they have their own distortions? When set up correctly with the proper crossover horns sound very clean and dynamic with very low distortion. To quote Parts Express "Many of the compression drivers available provide high-fidelity sound and low distortion that can compete with some of the best standard tweeters on the market…only much, much louder."