The Earth that Sonic the Hedgehog and Doctor Eggman call home is similar to our one, although the continents are shaped somewhat differently. The world is made up of several countries with their own unique cultures, which just so happen to almost perfectly mimic the cultures of most Earth countries.
The main difference to it and the normal world, however, is the presence of small, anthropomorphic animals. They aren't quite as widespread as humans, but they can be found all over the world, and are generally accepted to be not too different to humans. Many of these animals are stronger, faster and more durable than humans, which leads several of them into becoming super heroes.
The world is somewhat more technologically advanced than others, as well, with fully-sapient AIs not being unheard of, and several factions making use of robots. Eggman is, of course, the world's foremost expert on robots, but other people have cribbed his designs over the years.