Compassion for all beings is the foundation for all Tantric practice. The motivation to achieve enlightenment is born out of a desire to help others to awaken and to end the suffering for all beings. This practice is called Bodhichitta, which means "awakening mind." In Buddhism the mind is associated with the heart, not the head. Bodhichitta also is associated with wisdom and spaciousness. So to activate compassion, you awaken the heart with both wisdom and spaciousness.

Compassion is different from sympathy, which can sometimes cause a feeling of being over whelmed by the suffering of others. If you become overwhelm by such emotions you are now one of those who is suffering. If you are suffering you have lost  your equanimity. To regain it you need to let go of any attachment or aversion you have towards the situation and regain your own inner peace.