Price elasticity of demand is very important for the owner (or other policy-maker) of a supermarket because knowing the price elasticity of demand for various products helps you to determine the appropriate price for those products.
The law of demand tells us that the quantity demanded drops as the price goes up and rises as it goes down. But it does not tell us how much the quantity demanded changes for a given change in price. This is very important information for a store owner.
Imagine that you are selling a cut of beef for $5 per pound. People buy 100 pounds of it and you gross $500. Now imagine you raise the price to $5.50. If people buy 95 pounds (reduce their buying by 5 pounds), you will gross $522.50 and you will be happy that you raised the price. If they reduce their buying by 15 pounds, you only sell 85 pounds and you only gross $467.50. You will be unhappy that you raised the price.
This is what price elasticity of demand values tell you. They tell you how much the quantity demanded will change when you change your price. This means that they are clearly useful to whoever sets prices at the supermarket because that person can know ahead of time whether changing the price will result in higher or lower revenues.