Elasticity is a crucial part of economics because it shows the responsiveness of one variable to a change in another. For example the elasticity of demand answers the question of how much does quantity demanded change in response to a price change. In other words it would be percent change of quantity demanded when the price changes by one percent. Through the degree of movement, or the level of elasticity, we can see how important or valued a product is to consumers. Elasticity of supply is also related to the company having enough profit margin to drop prices or be able to produce or manufacture product according to demand.
When a change in price elicits a relatively large change in quantity demanded then the good is considered elastic. If there are only slight changes in quantity demanded in response to a change in price, then the good or service is considered inelastic. Elastic goods can be thought of as goods that the consumer does not care much about (i.e. luxury goods, goods with large number of substitutes, etc). On the other hand, inelastic goods are goods that the consumer cares a lot about (i.e. addictive goods, necessities, etc) so that even if the price changes, the consumer will continue demanding a similar quantity of the good.
The formula for the elasticity of demand is as follows:
e = P/Q * dQ/dP
Notice that dQ/dP = 1/slope
The concepts regarding elasticity of demand are applicable to other types of elasticity such as elasticities of inputs, cross elasticities, elasticities of supply, etc.