The bilge is the lowest part of a ship where the bottom curves up to meet the sides. The water that collects there is also called bilge. Since bilge is dirty and smelly, the word is also slang for “nonsense.”
On a large ship, some water inevitably ends up in the part that’s below the water line, the bilge. Because the bilge tends to sit there for a long time, sloshing around and mixing with oil, chemicals, waste, and cleaning products, it tends to stink. Periodically, the bilge is pumped out so the ship doesn't get too heavy and sink. Bilge is thought to be a variation on bulge, originally "wallet or bag," and later "ship's hull."