Pokémon Stadium 2, known as Pokémon Stadium Kin Gin in Japan, is a video game for the Nintendo 64. It features all 251 Pokémon from the first and second generations. It was released in North America as simply Pokémon Stadium 2, as it was the second Stadium game to be released there. In Japan, Pokémon Stadium Kin Gin was the third game of the Pokémon Stadium series.
While Pokémon Stadium 2 does have a storyline, progress in the game can be made by winning Cups in the Stadium and completing the Gym Leader Castle. When all Cups have been won and the Gym Leader Castle completed, the player's Rival will appear. Defeating the Rival will unlock Round 2, in which the player must re-challenge the Stadium, Gym Leader Castle, and the Rival in order to complete the game.
The player begins by choosing 6 different Pokémon. There are 250 different Pokémon to choose from; including some legendary Pokémon. Pokémon tournaments take place in the Stadium. There are four Cups to participate in. Each round consists of eight battles, and every Cup except the Little and Prime Cup consists of four rounds, named after Poké Balls, that must be cleared to win that Cup.
Source: Wikipedia, "Pokemon Stadium 2", available under the CC-BY-SA License.