The total pressure of a gas, such as air, is calculated as the sum or total of all the partial pressures of its component gases. For example, the air you breathe every day here on the surface is made up of a mixture of gases, mainly oxygen and nitrogen. The pressure of air/gas at sea level is 1 bar/ata, and it is approximately 21% oxygen plus 79% nitrogen (78% N2 +1% inert gas). However, an important variable component in the air you breathe on the surface is water vapor. At tropical temperatures and when the relative humidity is high, the partial pressure of water vapor in the air can be considerable (as much as 4%). However, the compressed air you use for diving has had almost all the water vapor removed, so at sea level, you can say the pressure of oxygen in your breathing gas is 0.21 bar and nitrogen is 0.79 bar, and the total pressure is calculated as 0.21 bar + 0.79 bar = 1 bar.
Open circuit works with a fixed amount of oxygen, but the oxygen partial pressure changes as the depth of the dive increases or decreases. For example, the 21% oxygen in a cylinder of air is affected by the pressure at depth and its partial pressure increases in direct proportion to the ambient pressure. For example, at 20 meters/66 feet (the depth limit for an Open Water 20 diver), the oxygen partial pressure is increased to 0.63 bar—three times its partial pressure on the surface—because the air you breathe at that depth has three times the density.
Partial pressure is important to know on a rebreather or open circuit nitrox dive, which are both covered in additional diver training courses.