The original Pokémon Red and Blue games included 151 Pokémon.
Those 151 creatures formed the first Pokédex, the in-game encyclopedia that players were encouraged to complete. The number includes Mew, a secret Pokémon that was not normally obtainable through ordinary gameplay in the original releases. Mew was added late in development and became the final entry in the first-generation Pokédex.
Red and Blue do not each contain every Pokémon as a catchable species. Some Pokémon are exclusive to one version, so players must trade with someone using the other game to complete the collection. The Game Link Cable made trading and battling between two Game Boy systems a central part of the experience.
Later generations expanded the Pokédex dramatically, which is why 151 is specifically associated with the original generation rather than the franchise as a whole. Pokémon Yellow uses the same first-generation Pokédex, although its story and starter arrangements differ from Red and Blue. The number 151 also explains the famous slogan “Gotta Catch ’Em All” in the early marketing era.