The Special stat is a stat that existed only in Generation I and partially in Generation II.
The Special stat accounted for what is currently known as Special Attack and Special Defense, determining how much damage a Pokémon both receives and deals when special moves are used. This created some balance issues, since a Pokémon could not be strong with and weak against a Special attack, or vice versa, at the same time, the same way a Pokémon might have strong Attack but weak Defense. With Generation II, the Special stat was outwardly split into Special Attack and Special Defense, meaning Pokémon could have different base stat values for both, and those stats were both displayed on a Pokémon's stat screen; however, individual values and effort values remained unsplit, so that there was only a Special individual value and Special effort values, which affected both the Special Attack and Special Defense stats. In Generation III, IVs and EVs were finally given both Special Attack and Special Defense values as well.
The Special Attack stat, or Sp. Atk and Spcl. Atk for short, partly determines how much damage a Pokémon deals when using a special move.
The Special Defense stat, or Sp. Def and Spcl. Def for short, partly determines how much damage a Pokémon receives when it is hit with a special move.