Price elasticity of demand is the most common form of elasticity. It measures the change in quantity demanded caused by a change in the price of the good. It’s calculated as a ratio of change in quantity demanded to change in price.

The following two graphs depict perfectly elastic and perfectly inelastic demand.

A perfectly inelastic demand means that the demand for the good remains the same irrespective of a change in price. This means that the consumers have no alternative to purchasing the good. An example is a lifesaving drug for which people will be willing to pay any price. A change in price wouldn’t cause a change in quantity demanded.
When price elasticity is -1 it’s called unitary elasticity. This is the price/quantity combination that maximizes the total revenue (price * quantity).