Pressure Vessels are also known as Pressure Tanks and have a pre-charged bladder style tank with a bladder inside. The bladders in the pressure vessels are usually made of rubber or vinyl and are surrounded by pressurized air.
Your water pump will push water into the bladder under pressure. When the pump shuts off, the water is held inside the tank by a one-way check valve in the piping system. A pressure vessel attaches to the outlet of a water pump. You will need some sort of switch on it (usually a mechanical switch) which turns the pump off when the system pressure reaches a pre-set point, sometimes this set point is fixed and sometimes it is adjustable.
When you purchase a pressure pump with a pressure vessel from Strongman Pumps, a pressure switch is included unless it is specified. Pressure vessels have a tyre valve attached to it and compressed air is pumped into it until the pressure is at a certain level. This level depends on the size of the tank.