Basically as ciaonzo said, a horn is used for impedance matching. What is impedance matching? Well, the material that the cone of your driver is made from is far denser than the air in which it's oscillating. This causes inherent inefficiencies when trying to move decent amounts of air to get low frequency output. What a horn does is by gradually radiating outwards, it tricks the speaker into thinking the density of the cone and density of the air are similar, which allows it to move into the lower octaves easier and with more output. Technically speaking, this is called impedance matching and what it means for us is that a speaker can turn high pressures at low displacements into high displacements at low pressures. How that works is that at the throat of the horn where the passage is narrow, it loads pressure there using some physics developed by Bernoulli about fluids. Once the pressure at the throat is loaded, the horn then expands usually exponentially, but as ciaonzo said, hyperbolic expansions and others are also in use. That means, as said, it builds a lot of sound pressure there for a relatively small amount of cone movement. As the air moves through the expanding portion of the horn, the sound unloads and creates a seemingly higher displacement of air, but at a much lower pressure.
Flared ports do not load and unload the air passing through them, and in fact, they are utilized to prevent that from happening, so no, a flared port and a horn are completely different.
So what I just described is the more technical reasoning behind what I said previously. By creating a larger displacement of air at lower pressure, the loudspeaker then makes the sound coming towards you less directional, which is exactly what happens when you're using larger drivers moving more air.
