One of the nice things about a water tower is that the pressure is not really affected by flow rate (unlike a traditional pump which has a limited power output and where the pressure drops off as flow rate increases).

Potential energy is stored in the tower. If more people turn on the tap, the potential energy just gets used faster. So long as the tank doesn't run dry, there will always be water pressure for everyone. Then a pump can slowly supply the tower during times of low use such as nighttime.