The relationship between the solubility of a gas and its pressure is a linear one, and can be described by Henry's law.

When a gas phase molecule hits the surface of a liquid it may be deflected back into the gas or dissolved into the solution, in the latter case becoming a solute particle. If a dissolved molecule reaches the surface of the liquid, a fraction will have enough kinetic energy to escape, and so particles are being exchanged across the liquid/gas boundary all the time. When the rate at which the gas phase particles enter and leave are equal you have a dynamic equilibrium, where the concentration in each phase becomes a constant value. The solubility is a measure of the concentration of the dissolved gas particles in the liquid and is a function of the gas pressure. As you increase the pressure of a gas, the collision frequency increases and thus the solubility goes up, as you decrease the pressure, the solubility goes down..