This is because they are mammals that live in water and need to be aware of their surroundings even when resting. Their eyes are adapted to be open underwater and they have a special membrane that protects them from the water.
While they may appear to be awake, manatees do enter a state of sleep where their brain activity slows down and their muscles relax. They usually sleep for short periods of time, and they often rest near the surface of the water so they can easily come up for air.