Although Bill correctly points out the expansion tank takes care of the increased pressure, it may be helpful for you to know how it does that so you understand that it's not extra water storage. Picture the expansion tank as a small tank having a rubber diaphragm across the middle (although there are some other designs). It has water on one side and air on the other. As your pump works it forces water into the water end and that forces the diaphragm to flex into the air side until it compresses the air to the pressure that turns off your pump. The next time you run water that pressurized air pushes back the diaphragm, the pump comes on and the cycle repeats. Hence you will notice the pump will not go off as soon as you close your faucet - it needs a couple of seconds to pressurize the system up to the shut off pressure.
Now, when your hot water heater operates the hot water expands and needs a place to go or it will either open the pressure relief valve or burst the tank. That's where the expansion tank comes in. The expanded water flows back into the system and the expansion tank diaphragm will expand to accommodate it, keeping the pressure in the system below the level of your safety pressure relief valve on the hot water heater.
Depending on what tank you buy, some are pre-pressurized and some have a schrader (bicycle) valve you use to add air. You'll want to keep the pressure about the same as the cut off pressure of your pump. You can play with it if your pump cycles too long after shutting off the faucet (too much pressure) or if it cycles exactly with the faucet (too little pressure, such that it's just acting as an additional tank with no expansion capability.)
Hope that helps.