From Bulbapedia, the community-driven Pokémon encyclopedia.
A map of the Kanto, Johto, Hoenn, and Sinnoh regions.
A region (Japanese: 地方 chihō) is an organized area of the Pokémon world.
In the main series
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 is the only region not to have its own Elite Four. It instead shares one with the neighboring Kanto region). Each one also typically has a Pokémon professor, who teach youngsters about Pokémon and give out starter Pokémon to them. There is usually a villainous team operating within the region, who uses 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, and in the culture of the people there.
In Diamond, Pearl, and Platinum, Professor Oak explains that 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.
In side games
The regions in the side series differ dramatically from the regions in the main series such as Johto and Sinnoh. Regions like Fiore and Almia are much smaller and have different cultures. They prefer Pokémon as pets instead of tools for battling. Pokémon trainers are not present in the regions. Pokémon are not kept inside Poké Balls and wild Pokémon can be seen wandering cities as well as routes. Pokémon Rangers act as authority, helping Pokémon and people in need. There are no 8 individual gyms, an Elite Four and Champion. However, Rangers can take the Capture Challenge to test their skills. Despite their peaceful natures, there is however, villainous teams that operate within both regions that capture and use Pokémon to further their goals of world domination. One such villainous team has been know to brainwash Pokémon using their advanced technology, causing them to lose their memories and wreak havoc.
The Pokémon Mystery Dungeon series takes place in a region that is not populated by humans and solely Pokémon. Most Pokémon live in dungeons as there is shown to be hardly any modernized communities among Pokémon themselves. The only towns shown are Pokémon Square, Treasure Town, and Shaymin Village, all of which are very small. Some of the Pokémon within them form exploration teams that explore dungeons and help Pokémon in need. There is an associated federation similar to the Ranger Union in Fiore and Almia that organizes all activities for rescue and exploration teams. The Wigglytuff Guild is where beginning exploration teams live and learn the basics. The Makuhita Dojo and Marowak Dojos are places somewhat similar to Gyms in the main regions where exploration teams hone their skills.
In the anime
Regions in the anime are much larger then their game counterparts. The regions are shown a number of cities and towns that are not present in the games. In some cases, some areas are moved to a different region from their game counterparts. For example, the Hoenn Battle Frontier in Pokémon Emerald was not in Hoenn in the anime. It was located in Kanto, with the different facilities scattered all over the region rather being located on an island.