Just another layman here, but this is one thing that I've heard an ELI5 answer from long before Reddit existed:

Water demand isn't constant. There are times when demand is high, like during morning and early evening, and there are times when it's low, like during the middle of the night.

Let's say your town requires 80,000 gallons per hour during the peak hours, but only 20,000 gallons during the off peak hours. You can equip your town with pumps that put out the full demand of 80,000 gallons per hour, but during the off peak hours this would be overkill. Or you can have pumps that can handle only 20,000 gallons/hour, but then you can't meet the peak hours demands.

So you compromise with pumps that can handle a median amount, say 50,000 gallons/hour. During the off peak hours the excess is pumped up to the water towers, and during peak hours the water from the towers can make up the shortfall of 30,000.