From the Super Mario Wiki
Trouter Bay is a large body of water that borders on an unnamed city somewhere on Mushroom World. It is named for the high concentration of Trouters that populate it. Bailiff Mouser claimed that Trouter Bay was scenic, more than likely aware he was lying.
Koopatraz State Prison used to be situated on an island in Trouter Bay, but it ultimately sank. As swimming in Trouter Bay is discouraged due to the risk of being eaten by Trouters, boats had to be used in order to cross the bay and reach Koopatraz. However, Mario, Luigi, Princess Toadstool, Toad, and Gramps all managed to swim in Trouter Bay for a brief period of time after swimming out of a drainpipe from the bottom of the island until they reached the surface.