Pokémon Green Version was released alongside Pokémon Red Version in Japan in 1996. The original Japanese Green Version & Red Version were basically the same, except for slightly different (perhaps worse) graphics.
Both games are exactly alike except that a handful of Pokémon (Pocket Monsters) are exclusive to each version. The two versions were designed to be bought by different people, who would then use Game Boy link cables to trade and battle their collected Pokémon.
The massive success of the game revitalized the Game Boy, and revived many returning franchises such as Monster Rancher and prompted Japan to port over new ones like Digimon. Many other games such as DemiKids and Mega Man Battle Network borrowed the "Two Version" format for their games as well.
You are a young boy in a world where creatures called Pokémon exist in the wild. Their purpose is to be pets, or caught and trained for competitive battle. One day, your neighbour Professor Oak offers you one of three Pokémon: Charmander, Bulbasaur or Squirtle. Once you choose, Oak asks you to fill up his Pokédex by seeing and catching as many Pokémon as possible.
Oak's nephew Gary (Shigeru in Japan) is on the same mission. While you're filling up your Pokédex, you are also looking to become the Pokémon Champion by defeating every Gym Leader in your country of Kanto, then defeating the Elite Four in the Pokémon League.
There are 11 Pokémon which are only found in this version.