The Star World is a sort of hub that connects various areas of the game. Once you have unlocked the respective Star Roads by beating the levels on the normal overworld the Star World levels, you can warp between them.
Star Roads can be found in five locations on the overworld: Donut Plains (beat Donut Secret House via the secret exit), Vanilla Dome (beat Vanilla Secret 1 via the secret exit), Twin Bridges (beat Soda Lake), Forest of Illusion (beat Forest Fortress) and the Valley of Bowser (next to Bowser's Castle, always unlocked). Using this, you can beat the game very quickly just by going through the Star World.
Finding the secret exit in Star World 5 unlocks another Star Road which leads to the Special world.