Compassion, in my view, is neither empathy nor sympathy, but requires both. Empathy involves responding to another person's emotions with emotions that are similar. Sympathy entails feeling regret for another person's suffering. Compassion, on the other hand, is caring about another person's happiness as if it were your own.
The challenge with this definition, however, is how easily it causes us to mistakenly infer that compassion therefore means. Compassion is NOT giving people what they want, or sacrificing ourselves. Compassion is Unconditional Acceptance. Compassion focuses itself only on the potential all people have for good, ignoring everything else.
Which will require endurance. The people for whom you care may refuse to stop suffering. They may rail against you for your efforts and treat you even more shabbily than others who don't care about them at all. Having true compassion for them is refusing to be defeated by such transient concerns.
HOW HAVING COMPASSION FOR OTHERS BENEFITS YOU
In the Lotus Sutra (the highest teaching of the original Buddha, Shakyamuni), luminous beings known as the Bodhisattvas of the Earth make a great vow to help all people attain enlightenment. In Nichiren Buddhism, a bodhisattva is anyone who manifests the life-condition of compassion.
This, then, is the ultimate goal to which I aspire: to expand my capacity for compassion and become a bodhisattva. The reason is simple: the feeling of genuine compassion for another person is, in my view, one of the most joyful experiences available to human beings. Further, only in the life state of the bodhisattva does it become clear how making the happiness of others the ultimate goal of one's life entails no personal sacrifice at all. Finally, I don't believe that indestructible happiness is possible to attain in isolation. How can anyone be truly happy while everyone—or anyone—else around them continues to suffer?