Avalon is the name of the entire continent the world of Pokemon-of-Avalon takes place in, hence the group name. It is the continent that King Alaric and his people from the original kingdom of Adonai stumbled upon and formed the new kingdom of Aether that became the capital city of a certain unnamed country that is also now called Aether. The continent is also home to the countries of Artiphron (Greece), Voluntas (Rome), Khetmaat (Egypt), Gāng Tiě (China), Sazanami (Japan), Samudaay (India), Gunjynh (Persia), Badiya (Arabia), and Gailamir (Vandals).
In addition, it is also home to the Veethfölnir Tribes (Vikings), Chanyu Tribes (Mongolians), Tonaltzintli Tribes (Aztecs/Incans/Mayans), Naklin Tribes (Inuits), Nizhoni Tribes (Native Americans), and Kalka Tribes (Africans). Finally, Pae'aina Tribes (Pacific/Atlantic islanders) live on the islands surrounding the continent.
Pokemon have always lived on the continent of Avalon, long before even recorded history.
2,000 years ago, in the area where the kingdom of Aether now is, a bunch of Pokemon (that are now known as the ancestors of the Nizhoni tribe of the Pelaruna) arrived from the moon via a meteor impact. They quickly adapted to the customs of the surrounding kingdoms and created their own, which became one of the most advanced civilizations on the continent. They also had a treasure known as the Celestial Stone; an object of unimaginable power, and like all objects of power, other people sought to claim it for themselves.
1,000 years after that, there was an enemy who everyone thought they could trust who attacked during the coronation ceremony of the new king. The new king managed to use the Celestial Stone's power to seal it away for the next millenium; however, it came at a cost. The Fairy-typing of certain species, including all of the kingdom's original inhabitants was all sucked into the rock, and it wasn't enough to stop the enemy from burning the kingdom into the ground and slaughtering almost everyone in the largest genocide in recorded history on the continent of Avalon. Though the other countries defeated the enemy after that, the old kingdom never recovered, and even today, the kingdom of Aether is thought to be haunted by the ghosts of all of those who were unjustly killed that horrible day.
Since then, no one trusts this currently unknown enemy, and today, it seems that really bad things are starting to happen across all the countries once again...