Simple...you fill it with nitrogen or compressed air and that additional pressure prevents the hydraulic oil from foaming.
The portion that holds the nitrogen is actually a rubber bladder to prevent air mixing with the hydraulic oil.
The other benefit of the reservoir is that it holds additional fluid that helps to prevent the shock oil from overheating, causing shock fade.
It may not do a great job, but it certainly does a better job than if it didn't have one at all.
The amount of pressure generally exceeds shop air pressures, so you may need to invest in a nitrogen bottle or take it down to a shop that can service shocks (tire repair shops often have them as well).
Don't fiddle with the shraeder valve, as just one tiny bump to see if it's got air will result in about 10-20PSI lost, a significant change.
To check and see if you have air in it without losing any, you can remove one mounting bolt from the swingarm or cushion lever and see if the shock extends fully after spring preload is removed from the equation.
It's a good idea to have it serviced relatively often so your shock is at its best anyway.

On the reservoir, you may see a little adjustment (some of them don't have one at all).
This is your compression adjustment, you can adjust this for a softer or harder damping force when the shock is compressed.
If you find yourself bottoming out landing a jump, try increasing the setting to prevent it.
If you're after a smoother ride, reduce the setting to allow the shock to compress easier.
On the shock itself, you'll probably find another adjustment.
This is your rebound adjustment, which changes the rate at which the shock extends.
It's useful in that you can adjust how the quad launches off a jump, and to reduce packing over choppy stuff (this is where the shock is going through rapid cycles, and if the compression stroke is slower than the rebound stroke, the rear end actually starts to get taller).
It takes a lot of time to get a shock dialed in to your specific riding style and particulars, but you'll be glad you did.

Any other questions or does that answer them?