A regional form is a permanent alternate form of an existing species adapted to a different region, with changed type, appearance, stats, and often Abilities, starting with Alolan forms in Generation VII. The original and regional forms share a Pokédex number and species name.
Pokémon Sun and Moon introduced regional forms in Generation VII, framed as species that adapted after moving to Alola. Alolan Raichu became Electric and Psychic and surfs on its tail. Alolan Marowak became Fire and Ghost. Alolan Vulpix flipped from Fire to Ice, and its evolution Alolan Ninetales became Ice and Fairy. These were not evolutions or battle transformations; an Alolan Sandslash is simply what Sandslash is in Alola.
Generation VIII added Galarian forms and gave some of them brand new evolutions, which the original forms never had. Galarian Yamask evolves into Runerigus instead of Cofagrigus, Galarian Corsola evolves into Cursola, and Galarian Meowth evolves into Perrserker instead of Persian. Generation VIII also added Hisuian forms in Pokémon Legends: Arceus, set in an older Sinnoh, and Generation IX added Paldean forms such as Paldean Tauros with three breeds and Paldean Wooper evolving into Clodsire.
In battle the form is a different Pokémon for practical purposes: different weaknesses, different movepool, different job. Breeding rules follow the form of the mother, and an Everstone lets a parent pass its regional form to offspring even outside its home region in later games. When you team build, always say which form you mean.
In play"Use the Alolan form here, since the Ice typing changes the whole matchup."