empathy is the ability to feel how another person must feel because that is how you would feel if you were in their place.
It is more than that, really, more a complete understanding that people are the same as you and have the same worries, and fears, experience sadness, happiness, love and jealousy and all those things. They may not feel them exactly the same way that you would, but they aren't rocks either, with no feelings at all. So a person with empathy knows that, and behaves to them with understanding, recognizing that they are people just like you.
And not only do you realize that they are people, as a thought, an idea that you can say with words. It isn't something that you just think, well no duh, they are people. You feel it. It is part of how you treat others without even thinking. It makes you feel terrible if you do a bad thing to another person, or to an animal, or pretty well anything that can feel pain or remorse and sadness. So you try to help people, to make their life better just as if it were your life that is being made better, even though it has nothing to do with you.