The Long Jump is one of Mario's many techniques that he uses in most of the 3D platforming games. Mario and Luigi can use it to clear long gaps to reach far away platforms, while still staying close to the ground for obtaining coins. To use it, Mario must run forward and, while he's running, press 'Z' and then the 'A' button. Mario will then be able to propel himself forward.
This move was eliminated from Super Mario Sunshine, because F.L.U.D.D.' s Hover Nozzle will carry Mario across the gaps he'd normally have to jump across.