What is compassion? Compassion is seeing yourself in another, and seeing through any illusions the person is holding on to. "Do unto your neighbour as you do unto yourself" was said because your neighbour is yourself. Every thing is just yourself in a different form.
Seeing Through Illusions
Compassion is the love that arises from seeing yourself in another, that sees through any illusions of another person.
Compassion arises when you see someone for what they really are - consciousness that is one with you. You can then see that anything covering this up, such as anger or fear, is not them - they are just confused about who they are.
When someone exhibits egoic behaviour you can see that is is just ego, not them. Compassion arises from this recognition - they are possessed by their own thinking mind, and believe they are something they are not.
Compassion comes when you take your"self" out of situations - someone is no longer acting toward you - attacking, criticising or blaming you - their bodies are just acting, as your body acts.
As you take yourself out of situations and stop looking at things from the concept of "I" you see things as they actually are - and compassion arises from here.
Common Compassion
A more common answer to "what is compassion?" is "feeling sorry" for people who are in pain or in some kind of bad situation. I do not think this is what real compassion is. It can involve judgement of the other person, rather than a pure seeing.
When you "feel sorry" for someone, the feeling becomes more personal, there is an "I" that feels sorry for "someone else". All it sees is pain. Action from here may feel compassionate, but can sometimes go "overboard" and prevent any useful change occurring for the other.
This compassion can also be selective - e.g greater for friends than it is for strangers. Also this compassion can diminish if you believe your sense of self is being threatened.
Real compassion goes beyond that, and sees through the illusions of the person or the situation. It is selfless. It sees directly that all individuals concerned are part of the same consciousness, and that same consciousness is pure, peaceful and eternal. Any painful manifestations arising out of this are just from errors or misperceptions by an individual.
The pain is seen, but is not taken as seriously as it is in a more common view of compassion. Healing is far more likely to emerge from here.
Do Not Force Compassion
The answer to what is compassion may vary depending on who you ask. If you try to be compassionate or try to cultivate compassion, you may have difficulty.
True compassion arises from being your true self. It is just a by-product of being conscious.
When you are your true self, you recognise your self in others. Anything covering up this truth in others is seen as not real. This is compassion.
The main thing is to remain as the timeless space in which everything arises, in which your thoughts, emotions or any sense of "I" arises. From here you are at peace and can automatically recognise the truth of other people and the illusions of other people. Surely the most genuine compassion will arise from here.