What does the Price Elasticity of Demand measure? How is it calculated? And why is it important?

Price Elasticity of Demand measures the responsiveness of quantity demanded by consumers after a change in price of the product. At A-Level this is measured via two points on the demand curve A and B. The percentage change in quantity going from A to B divided by the percentage change in price going from A to B is the coefficient of the price elasticity of demand. This is important at a supply level in terms of firms actions. If firms face consumers with high price elasticity of demand they can't charge high prices without seeing a drastic fall in quantity demanded, which would hurt revenues as the high prices would not offset falling quantity. So PED helps us predict market behaviour. More detailed answers could go on to talk about how PED will affect tax incidence, and also provide the economic intuitions as to why this is true.