I like the definition of empathy from The Greater Good Magazine the best. It is: The ability to sense other people’s emotions, coupled with the ability to imagine what someone else might be thinking or feeling.
The most common mixup with empathy is to mistake it for sympathy. Empathy is you putting yourself in someone else’s shoes. This is opposed to sympathy where you’re letting them know you’ve experienced what they’ve experienced, and you know what it’s like.