A Pokémon's spirit is sent to the Voidlands when its body has been turned to stone in the Pokémon world. The Voidlands are strongly connected with Dark Matter, whose goal is to "return the world to the void". They are also home to Void Shadows.
Once the player has returned to the Pokémon world after clearing the Voidlands' four dungeons during the main story, the Voidlands become inaccessible; the dungeons can subsequently only be revisited through Pelipper Island, where they are listed as part of the Water Continent in the dungeon list.
Coming across various runes deciphered by the partner, the player learns that Dark Matter is responsible for the current events in the Pokémon world. Dark Matter appeared in the ancient past, but was stopped before it could spread its influence and destroy the planet by possessing a landmark known as the Tree of Life. Some of the group are captured by Void Shadows, blob-like minions of Dark Matter capable of assuming the forms of Pokémon. The rest of the team manages to reach the peak of Reverse Mountain, where they find that the Door to Hope, the gateway to their world, is heavily guarded by more Void Shadows. While the rest of the group holds the Void Shadows back, the player and partner can finally return to their world.
It is stated that the enemy Pokémon found in the Voidlands are not real Pokémon, but illusions made of hate manifested into a physical form.
Trivia
Even though the enemy Pokémon in the Voidlands are supposed to just be apparitions, the Connection Orb still reacts to them.
This article is part of both Project Locations and Project Sidegames, Bulbapedia projects that, together, aim to write comprehensive articles on the Pokémon Locations and Sidegames, respectively.