The purpose of cruise ship stabilizers is to reduce the the rocking motion of the ship. They help a ship move more smoothly, which cuts down the chance of seasickness for passengers. When there is a great deal of movement, it can cause a discrepancy between what a person sees and what her inner ear senses. This is what causes seasickness. The smoother the ride, the less chance for this to happen.
Cruise ship stabilizers extend out below the water line on the port and starboard sides of the ship. They prevent it from rolling to the left and right as it moves through the water. They act much as do airplane wing flaps, which can be adjusted to reduce turbulence. Although no stabilizers can prevent 100 percent of a cruise ship's movement, they can significantly reduce it. This is especially desireable in rough conditions when the waves are high or the wind is strong.
Cruise ships usually use a fin stabilizer system with one or two sets of fins that look almost like stubby wings. The fins can adjusted based on the sea and wind conditions to maximize their effectiveness. This is typically done by an electronic control system. Modern cruise ships have hinged fins that can be moved out of the way when they are not needed or when docking.