Empathy refers to the ability to feel and share emotions with others.
An empathic person will cry when they see someone being sad, or will celebrate when they see someone succeed and be happy as if it was their own success.
Empathy leads to generosity (cf generosity). It stimulates mutual aid because it encourages us to identify with others, to put ourselves in their shoes.
We all feel empathy, some people feel it more than others.
Empathy allows us to understand what the person in front of us is feeling. It's necessary to build a solid relationship, with a friend or a lover, and to resolve conflicts.