Note: This page and the other two pages under the "Headcanon" header are dedicated to giving you, the reader, a crash-course in the stuff that make up the background of the fanfics on this site. It's not necessary to read through all of this and remember every little detail, but it might help.
The world is an alternate Earth. Basically, there's the typical flora and fauna (like cats, birds, fish, et cetera), but the populations of fauna are slightly less dense than in the real world because of animals' inability to successfully compete with Pokémon for food and other necessities. Ergo, the dominant wild species of any area (besides humans) are usually Pokémon.
Additionally, each region is a region in the literal sense -- as in, a part of a country but not a country by itself. For a real-world example, it's like considering the northeastern states of the US a region called New England. It's not a state itself or a separate country. It's merely a group of places that share the same kinds of geography, climate, and culture. The same thing goes with the canon regions. Kanto is essentially the counterpart of the real Kanto in Japan. Johto is equivalent to Kansai, Hoenn is Kyushu, and Sinnoh is Okinawa. Meanwhile, other places like Orre are the equivalent of places outside of Japan. (Orre itself, for example, is the equivalent of Arizona and other parts of the Southwest.)
Hence, all of the countries in the real world exist but aren't replaced by the canon locations. There's still a United States, an England, and a Japan, among other things. However, things are slightly different in terms of names and culture as a result of the history of this universe.
Due to the events further explained on the History page, Japan has been largely westernized. It's now a melting pot with just as much European and American influence in the nation as there is Asian. The official language is Common, a language that was based mostly on English and, to the viewer, sounds pretty much like English. (The written language, however, resembles a blockier version of the Japanese writing system. This comes mostly as a result of the close ties between both nations at the time of the treaty's signing.) However, a few people still speak Japanese or other real-world languages, particularly those who have remained largely traditional.
There is no real set religion thanks to the melting-pot lifestyle throughout the Japanese islands. It's just as likely to find someone who claims to be Christian as it is to find someone who worships exclusively Pokémon. For the most part, though, the more popular beliefs usually involve the legendary Pokémon. In addition to this, no two regions are alike in terms of belief system, rendering a national religion fairly impossible.
The simple form of it is that every region has variations in local legends, and as such, while worshiping Pokémon is considered an overall religion called "Pokéism" by the government, there's separate denominations that people identify with first, each possessing a different flavor and basis. For example, Sinnohism is a few thousand years old, but rather than rooting itself in purely Japanese traditions, the modern form resembles Christianity more than anything else, complete with services held in large churches and the philosophy that Arceus, the ultimate god of the faith, shaped the universe in a short time period. Johtoism, meanwhile, is a following that seems to base itself more on Shinto traditions. While Sinnohism holds services in churches, Johtonian centers around ornate temples, concepts that heavily involve the legendaries as kami (supernatural and all-powerful spirits of nature), and the worship of Ho-oh (the emperor of the sun and Heaven) and Lugia (the guardian of the moon and the sea) as the highest-ranking kami.
Besides that, the culture of the Pokémon world differs from that of the real world in that children are treated much differently. From an early age, children are raised to be self-reliant in order to participate in a tradition that nearly every single member of that society undergoes at the age of ten or eleven: a Pokémon journey. In an effort to honor the past (in which humans and Pokémon lived in harmony), most adults encourage the younger generations to apply for an official trainer's license at the minimum age of ten and go out to experience the world. This period of a person's life is seen as a time of self-discovery and growth mostly because, ultimately, young adults who participate in this tradition are usually cut off from their homes. That is, their income comes from their own winnings (if not an allowance from their families), and they're expected to be able to cook, clean, and generally fend for themselves. As a result, a trainer may travel the world and undergo unique experiences they couldn't possibly gain from sitting in classrooms, but the main lesson (besides that all creatures of this world should live in harmony) is to develop skills they'll need later on in life.
At around this time, online courses are offered to trainers on the road. The lessons tend to be looser than in the classroom with fewer a week and very few deadlines. Still, in order to maintain his or her license, a trainer under the age of eighteen is expected to complete a certain number of hours of class work a month. (Trainers typically use time spent in Pokémon Centers to do this.) Additionally, some young adults choose not to pursue a long-term career in Pokémon training and can be welcomed back to schools in their hometowns -- provided they take a reentrance exam in order to be placed in an appropriate year.
Because the franchise focuses on the observations of a ten or eleven-year-old, government takes a back seat in canon. However, the government of this world exists and operates essentially the same way as the real-life Japanese government. There is a prime minister and a cabinet usually elected by the people as well as a royal family operating as figureheads. The capital is located in Tokyo City, an average-sized, bustling area not far from Saffron. Laws are essentially the same as they are in the real world, barring those concerning adulthood and education (which, as implied above, are changed thanks to the concept of Pokémon training) and adding a number involving Pokémon. (Theft of another trainer's Pokémon is a serious offense, as is the capture of wild Pokémon by unlicensed trainers -- hunters or poachers -- for the sole purpose of selling them. The intentional killing of a Pokémon is also comparable to homicide.)
Thus, it's worth it to say that the Pokémon League is not the government. Rather, the Pokémon League is seen as a sports league, one of the most popular (if not the most popular) worldwide. Leagues exist in every country with separate leagues for each region.
For everything else, there's canon.