Compassion comes from clearly seeing the state of how others are. Shifting your attention away from being concerned with merely yourself, you begin to tune into how other beings feel. Soon you realize that their aims and what they actually manage to achieve are in a total contradiction.
Everyone wants to be happy and free, but the involvement pursued through thought, word and deed for the most part create future pain, future entanglement. When one really sees this clearly, the sense of compassion becomes overwhelming.
Tulku Urgyen Rinpoche
Along with love, compassion is the face of altruism. It is a feeling from deep in the heart that you cannot bear others' suffering without acting to relieve it. As compassion grows stronger, so does your willingness to commit yourself to the welfare of all beings, even if you have to do it alone. You will be unbiased in your service to all beings, no matter how they respond to you.
His Holiness the Dalai Lama
By accustoming your mind that there is no time to waste
When a life of respites and enrichments is so difficult to find,
Turn from your obsession with the appearances of this life.
By thinking over and again about the problems
of recurring rebirth
And that the laws of behavioral cause and effect
are never fallacious,
Turn from your obsession with the appearances
of future lives.
When, by accustoming yourself in this way,
you never generate, for even an instant,
A mind that aspires for the splendors of recurring samsara,
And you develop the attitude that day and night
always is interested keenly in liberation,
At that time, you have generated renunciation.