This ability to see things from another person's perspective and sympathize with another's emotions plays an important role in our social lives. Empathy allows us to understand others and, quite often, compels us to take action to relieve another person's suffering.
While people are generally pretty well-attuned to their own feelings and emotions, getting into someone else's head can be a bit more difficult. The ability to feel empathy allows people to "walk a mile in another's shoes," so to speak. It permits people to understand the emotions that others are feeling.