After the events of Super Mario Bros. 3, Mario, Luigi and Peach visit Dinosaur Land for a vacation, but upon arrival discover Bowser and his army have invaded the island and kidnapped it's residents, and the princess is taken again.

Mario and Luigi team up with their new friend Yoshi to take down Bowser and the Koopalings, saving Peach and Yoshi's friends that are trapped across Dinosaur Land.

More about Super Mario World on Mario Wiki