It's called an accumulator. It's a tank that fills with water under pressure, and that water pressurizes a gas or a spring, and this pushes back on the water in your system so your pump doesn't have to.
Most systems (when on and not connected to city water) detect a lower water pressure, which causes the pump to turn on and re-establish the higher pressure. Once the pump has gone over the threshold of highest pressure, it turns off. Behind the scenes, the pressurization process pushes water into the accumulator, compressing the gas inside -- remember that liquids (generally) are incompres