It's similar to storing energy by inflating a balloon.

When you inflate a balloon, you are opposed by the tension in the skin of the balloon. You could then use that stored energy to do work if you wanted. E.g. you could make the inflated balloon blow air into a little wind turbine that would, in turn, light a small LED.

With the underwater system, you are inflating a bubble that is held captive in a concrete chamber. The force that opposes you is water pressure. The deeper underwater, the greater the water pressure, so the more power you can store with the same concrete vessel.

EDIT: Energy would also be stored through air compression.