A pressure tank is a vessel with an internal bladder which holds water under pressure.
Pressure tanks come in a variety of sizes and are also referred to as an accumulator tank as they accumulate water. With a pressure tank on your pump system the pressure switch is not tripped so often which in turn quietens the pump, reduces water hammering, pump cycling and will give you a much more consistant flow rate at your outlet. When you turn your tap on the excess water held or accumulated in the pressure tank is released first and your pump doesn't have to turn on until the stored water is used. A pressure tank therefore will lengthen the life of your pump and your battery as they are not turned on as often.