The home-made submarine that we have just built has an apparent density that makes it float in water. When you press the bottle, due to the almost uncompressibility of water, the volume of air contained inside the "submarine" decreases because it is compressed. Therefore, the "submarine" apparent density increases causing it to submerge. When you stop pressing the bottle, the air pressure returns to the initial state and the air volume inside the "submarine" increases. Then the apparent density decreases and the "submarine" begin immediately to emerge.
The true submarines work in a similar way, using pumps of water that suck water inside or remove it outside to submersion or emersion, respectively. As you see, the science is always there. That is a fascinating world!