A region (Japanese: 地方 chihō) is an organized area of the Pokémon world. There are at most sixteen known regions that have appeared in the various Pokémon canons.
The regions are structured similarly. Typically, a region will have its own Pokémon League, comprised of eight Gym Leaders. Once these eight are defeated, Trainers can challenge the regional Elite Four, which may or may not be shared with another, nearby region (so far, Johto does not have its own Elite Four, as it shares it with that of Kanto). Accordingly, each one also has a Pokémon Professor, who teaches new trainers about Pokémon and gives out starter Pokémon to them. There is usually a villainous team operating within the region that use Pokémon to further their goals.
Though there are many similarities between them, there are some major differences between the regions, such as what Pokémon are located there and what legends there are waiting to be uncovered. Visitors from another region quickly realize that the region they are visiting is far from their home, both in the way of the climate, distance and location; and in the culture of the people there.
Sinnoh, Kanto, and Hoenn (and probably Johto and others) are part of a larger country, whose name has yet to be revealed. This concept is similar to the regions of Japan, which the Pokémon world has been modeled after, and from which the Pokémon nation's Kanto region takes its name. Unova is known to be located far away from Kanto and Johto, and as such may not be part of this country.
Presently however, onto the Kanto and Johto regions are made readily-accessible to starting trainers.