Why does a submarine's density decrease when it pumps water out of its floatation tanks?

Water is denser than air. As the water is pumped out, air replaces the space that was occupied by the water. Therefore, the total density of the sub decreases. The above answer is correct. Here is a little more detail.

As you may be aware density is a function of mass and of volume. It's mass per unit of volume. If you had a pan full of water and a similar pan which was empty, the water filled pan would weigh more, though the overall volume would be the same. Hence the density would be greater.

When the submarine 'pumps out' the water it is replaced by air. Because air is less dense than water, it reduces the overall density of the vessel. Consider that the submarine is a vessel, as in a ship, and also a vessel, as in something that holds something else, like a cooking vessel. The submarine is a closed vessel; it has a fixed volume set by the hull. But by pumping water into or out of its internal tanks, it can change its total mass. If it pumps water in, it is increasing its total mass, and this will increase its density (as the volume stays the same). Pumping water out decreases the submarine's total mass, and its density will go down.