Air regulators are pneumatic devices that receive air at any pressure within its tolerance, and then dispense air of a pressure no greater than their intended output. In other words, air comes in at a higher pressure, and departs at a lower pressure in most circumstances. For the purposes of this article, everything that comes before the air regular is ‘upstream’, and everything after it is ‘downstream.’
Air flows from an air compressor somewhere upstream, and it may or may not interact with other upstream elements. When it reaches the air regulator, a system of springs and an internal diaphragm ‘pushes back’ against the incoming air, offering enough resistance that only a set volume of air (and thus, a set air pressure, since air pressure is calculated by volume within a given area) moves downstream. So long as the upstream pressure is enough to open the diaphragm, and not enough to tear the air regulator off of the device altogether, the downstream pressure will be constant regardless of how the upstream pressure changes.
This is a hugely vital function, because many pneumatic cylinders would be harmed by overly powerful air, or at the very minimum the jobs the cylinders are doing would be done poorly if they were done too quickly. For example, without an air regulator, a pneumatic cylinder attached to a carefully-balanced load might jolt upward too quickly and disturb the load it was lifting.
The air compressors have a ‘cutoff point’ at which they stop compressing air, instead allowing the air already compressed into their reservoir to do the work. Air regulators will cause the upstream system to back up such that the upstream pressure will eventually build up and cause the compressor’s cutoff point to trigger, stopping the compression until that high-pressure air has had a chance to work its way through the regulator enough that the air compressor restarts — but the downstream pressure from the regulator never changes until the entire system is shut down and the diaphragm finally closes.
The answer to the title question, then, is simple: you need an air compressor not only to protect delicate devices or delicate work from variations in the upstream air pressure, but to reduce the amount of air that your compressor has to process.