Price elasticity of demand is a measure of change in quantity demanded of a commodity relative to a change in its price. If the demand is inelastic, an increase in price results in increased revenue. If the price rise results in decreased revenue, the demand is elastic.
Knowing the price elasticity of demand, a firm can decide on an optimum price level of their commodity to achieve their revenue targets. Price elasticity information can help them decide how much price reduction is necessary to increase revenue to a certain target, or what level of price increase will be optimal (since extra revenue from a price increase may be wiped out by decreased demand).
The knowledge of price elasticity of demand also helps firms in devising their marketing strategies and targeting niche segments. An example is high net worth individuals whose demand for luxury is inelastic and hence hotels advertise suites to them. On the other hand, budget travelers have an elastic demand and hence are targeted for 'Standard' rooms.
Price elasticity is used to how elastic (or responsive) that firms are to a change in price, assuming everything else is held equal (ceteris peribus).
Businesses are very interested in this type of information because it can help them determine where the best price to sell is (where they will make more money). On the graphs, a part of the line is elastic, inelastic, and unit elastic. If it is elastic, then the more firms produce, then total revenue (TR) goes down. If it is inelastic, then if total production goes down, TR goes down as well. However, if it is unit elastic, then if the production changes, then the TR does not change. In short, what I am trying to say is that firms can use Price elasticity to determine how much of a product to produce in order to maximize profit and total revenue.
Hope this helps.