We know about Hogwarts where all the British wizards and witches go to train and then there is Beauxbatons in France and Durmstrang somewhere in Scandinavia which takes students from the surrounding countries, including of course Victor Krum’s homeland Bulgaria. There is also mention of South American and Japanese schools on the Pottermore website but still that is a lot of nations that aren’t catered for. Most notable by their absence are the three countries with the biggest population; China, India and the USA.
In the case of America, at least, the need for a school of witchcraft and wizardry more or less died out following the Salem Witch Trials in 1692. Even though only twenty people were killed and the trials were centred around Massachusetts, the hysteria generated in Muggles spread across the whole country and the magical population found themselves living in a climate of oppressive paranoia. Those witches and wizards who could get out of The States did so but most were forced into hiding.
Of course as Sirius Black and Peter Pettigrew can testify the best way for a witch or wizard to hide is to train themselves to take the form of an animal. Pettigrew, we know, stayed unchanged in his animal shape for many years and so too did a lot of those living in fear of persecution and death at the hands of packs of sanctimonious Muggles.
Not believing it safe to ever take human form, the wizards and witches bewitched their little animal mouths, throats and hyoid bones to enable speech and found that they could now exist perfectly comfortably this way. They developed large communities and whole societies happily living their lives away from the curious glare of people. They eventually began to start families without transforming back to their original states.
Unfortunately over time and across generations the true nature of these witches and wizards became myth and was eventually totally forgotten by their own kind. The children of the children of the children of the children of the children of the children of those original animagi could no longer remember the origins of their ancestors.
They knew they were different from other animals but did not understand why and soon just stopped questioning it. A wide population of intelligent talking animals, mostly but not exclusively cats (originally easy to keep an eye on the Muggles), birds and rodents (easy to stay hidden) was established in North America. The vast majority of these kept their mouths shut in public but a few of the bolder ones actually did start to communicate with humans. Very occasionally the odd talking animal would be accepted into a home environment and would end up living with them as a family member. Stuart Little is one such beast.