Yoshi's Island is where your adventure starts. You'll start off at Yoshi's House and have the option of going to the left (Yoshi's Island 1) or the right (Yoshi's Island 2). While going to the left eventually leads to a dead end, completing it will prove to be incredibly useful later on in your adventure. If you just wish to hurry, however, you can skip it and start off to the right. Things will be minimally harder but the game can still be completed without much difficulty this way.
This world serves as an introduction to Dinosaur Land, and allows you to get familiar with the game mechanics a bit before wandering into more dangerous territory. The castle is inhabitated by Iggy Koopa, and beating him grants you access to the next world, Donut Plains.