The events of Yoshi's Island take place in the past.
Mario was one of two twin brothers whom the evil Magikoopa Kamek tried to kidnap. Kamek kidnapped one of the brothers, but the second, Mario, fell down on Yoshi's island, where Yoshis live. The Yoshis decided to carry baby Mario and to bring him to his parents. But Kamek has sent troops and hordes of monsters to stop the Yoshis and to kidnap Mario.
In the game, players control the differently colored Yoshis most of the time. Mario is a helpless baby unless a star that makes him invincible is collected. As a Yoshi, players can swallow enemies to make eggs; these eggs are used for attacking other enemies and activating switches. Yoshi can do a flutter jump to clear large gaps that a regular jump can't. Players can also pound the ground for attacks and also flipping certain switches. Additionally, Yoshis can transform into vehicles, such as a helicopter, submarine, or a train. If Mario is dismounted from a Yoshi, a countdown will start, and Yoshi must catch the baby before Kamek's servants kidnap it. When Mario is invincible, he doesn't ride on Yoshi and is immune to attack. While invincible, Mario can run up certain walls.