Chocobo World is a mini-game that was originally for the PocketStation in Japan. In the mini-game you control a Chicobo called Boko and is assisted by Cactuar & Moomba.
You must first find Boko in the main Final Fantasy VIII game; this is done by completing a Chocobo Forest, afterwards Chocoboy will offer you Boko who will follow the Chocobo you ride on the world map.
From this point on, Chocobo World becomes an option on the Save Game menu, selecting this option allows you to send Boko to Chocobo World, bring him home, start over with a new Chicobo and learn how to play.