They spend large parts of their day outside of water. As long as they are kept moist, they can breathe through their specialized skin and also by gulping in air —hence their constant mouth agape expression.
Their stiff pectoral fins are their main means of locomotion on land; their pelvic fin is fused into a single suction cup like structure, which helps them hold onto slippery surfaces when they’re traveling up a slope.
They make burrows by gulping in mouthfuls of mud and spitting them out. Mudskipper burrows can be up to 40 cm deep, imagine the number of mouthfuls of mud did that took!