Breathing into water, per se, doesn't help. The air blown into the system is lightly pressurized, and this pressure helps inflate lungs just like inflating a balloon.

The water bottle is there because it's difficult to control the amount of pressure. Sinus tissues and lungs are very delicate, and pressurized air also messes with blood/gas ratios, so it's important to use the minimum pressure you can get away with. The bottle of water allows the pressure to be controlled simply and precisely, by adjusting the depth of the hose.