What is really more important than an increase in inlet air pressure in an engine, is any increase in air density you can achieve. Normal air is about 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.038% carbon dioxide, and the rest is small amounts of other gases like methane, etc. Without getting too far into heavy chemistry, every gram of air contains a certain number of oxygen molecules and can therefore combust a certain mass of fuel efficiently.
It can be a difficult concept to grasp but air does have weight or, more correctly, mass. And the density of a material is the mass of a standard volume of the material, say 1 litre. For water, its usual density is 1000g/L. For 'standard' air, at sea level (a pressure of 1 Atmosphere or about 1.0bar absolute) and at 15°C, its density is 1.225g/L. But air, unlike water, is compressible. That is, you can force a greater mass of air into the same volume. So, at a pressure of 2.0bar absolute (twice normal sea level pressure) a litre of air, still at 15°C, would have a mass of 2.450g and so its density would be 2.45g/L.
So, again, it all looks good. An engine running at 2.0bar absolute inlet pressure (1.0bar of boost) is ingesting air at twice the density and hence twice the oxygen content of its NA cousin, right? Well no, unfortunately. Did you notice the extra proviso in the paragraph above: "at 15°C"? This now makes all the difference. Temperature is intimately tied up with pressure and volume when it comes to compressing gases. After all, recall that compression ignition engines only work at all because air gets very hot if you compress it a lot.
So, in this process of increasing the pressure of the inlet charge to an engine, we invariably heat it as well. Therefore, the increase we get in air density is never as good as you might think just looking at the increase in pressure over 'normal' air pressure. Temperature effects will always come into play to reduce the potential density gain. We'll talk about this issue in more detail later.