If you have a hot water boiler system (not a low-pressure steam boiler - there is a huge difference between the two) or a chilled water system (not many chilled water systems in residential but I have seen them) then you have a closed loop piping system that runs to either convectors, radiators, or a coil or two somewhere in the system where the main heat exchange process takes place. That is a closed loop where the water runs to these convectors or coils to provide heating or cooling. Furthermore, it is important to maintain the proper pressure inside that closed-loop piping system — an Pressure Vessel helps to maintain the proper pressures in the loop.
Inside this piping is water (sometimes a water/glycol mix but that is mainly in commercial applications), and when water heats and cools down, it expands and contracts. Furthermore, the piping system, along with the parts of the boiler or chiller that has water, cannot handle this expansion and contraction with breaking or busting open. Therefore in every hydronic system, there is an Pressure Vessel to handle this expansion and contraction. Furthermore, an Pressure Vessel is a shock absorber that absorbs this expansion and contraction of the volume of the water.
It is critical that pressure vessel receive periodic maintenance. Furthermore, for bladder-type pressure vessel maintenance should include: