A Mythical Pokémon is a rare Pokémon that, in the main games, is normally obtainable only through official distributions such as events, codes, or special promotions rather than regular gameplay, including Mew, Celebi, Jirachi, and Arceus. Mythical Pokémon are officially classed separately from Legendary Pokémon in Japanese materials and, since Generation VII, in Western ones too.
The category exists because of distribution, not power. Mew was added to Generation I in secret and revealed through a magazine promotion, and that pattern held for decades: Celebi through events, Deoxys through an event ticket to Birth Island, Darkrai and Shaymin through event items, Victini through the Liberty Pass. If you played a game years after release with no event running, most Mythical Pokémon were simply unavailable to you.
Many Mythical Pokémon share a stat fingerprint of 100 in every stat, including Mew, Celebi, Jirachi, Manaphy, and Victini, for a 600 total, though later additions broke the pattern freely. Phione also shows the category's odd edges: it can be bred from Manaphy, the only Mythical that produces eggs, and Phione itself is classed as Mythical despite hatching like a normal Pokémon.
The rules have loosened recently. Pokémon Omega Ruby and Alpha Sapphire put Deoxys in the Delta Episode storyline, the first time a Mythical was catchable in the normal story, and Pokémon Legends: Arceus let players catch Arceus, Darkrai, and Shaymin in game under save data conditions. In battle facilities and official competition, Mythical Pokémon are usually banned alongside the strongest Legendary Pokémon.
In play"You cannot just catch a Mythical Pokémon in the grass, you had to get it from an event."