The compassion we feel normally is biased and mixed with attachment. Genuine compassion flows towards all living beings, particularly your enemies. If I try to develop compassion towards my enemy, it may not benefit him directly, he may not even be aware of it. But it will immediately benefit me by calming my mind. On the other hand, if I dwell on how awful everything is, I immediately lose my peace of mind.
When something needs to be done in the world to rectify the wrongs, if one is really concerned with benefiting others, one needs to be engaged, involved. This is action out of compassion.
A man of good sense but of little faith, whose compassion seemed to lead him to church as often as he went there, said to me; 'that he liked to have concerts, and fairs, and churches, and other public amusements go on.
The essence of all religions is love, compassion, and tolerance. Kindness is my true religion. The clear proof of a person's love of God is if that person genuinely shows love to fellow human beings.
For an act to be moral the intention must be based on compassion, not duty. We do something because we want to do it, because we feel we have to do it, not because we ought to do it. And even if our efforts fail - or we never even get to implement them - we are still moral because our motivation was based on compassion.
Can you imagine if you really let it in that you are not a problem to be solved in any way? Imagine you knew that anything that would tell you otherwise is just a movement of thought in the mind that says "Whatever is, isn't the way it is supposed to be." So the biggest act of compassion starts within. And when the self is no longer seen as a problem, this is called "the peace that passes all understanding."