Basically, a horn increases the sound output from a speaker. It does that by reducing the mass of air directly in front of the driver allowing it to move that mass of air more efficiently. This happens more effectively in the lower frequency range because it also stops the wave from propagating outwards to the sides. The highest frequencies are mostly unaffected because they beam directly forward.
That extra output gives you more flexibility when you are designing the crossover. That lower end boost may allow you use a lower crossover point than you could if flush mounting the tweeter.
However, the horn can also dramatically change the way the speaker sounds, so that's something to keep in mind.
Horns also work for midrange drivers and woofers, but have to be much bigger.

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