what is the inflater in the trunk for?

It is a air pump, you should have a hose with it. (for soccer/footballs etc, bike tires and there should be a long hose to "top" up your tires on the car) If you have "air" suspension, I do believe that it is intertwind with the air suspension.

Its for the auto leveling suspension that you car has. It also helps with the dampening rates of the shocks. If you put a lot of weight in the car you will hear it run to level the car out, also when you drive it will run from time to time. It also has a secondary use as a pump to fill tires, toys, whatever else.

How would I know if my rear shock has an air leveling system, I have 1998 Boneville SSE and it also has that air pump.