Karuna is compassion’s technical name in Indian traditions. It is distinguished from Metta (lovingkindness): metta wishes beings well; karuna responds specifically to beings who suffer.
In Mahayana Buddhism, karuna paired with Emptiness is the complete formula. The Bodhisattva vow is karuna made explicit: I will not enter final liberation until every being is free. Its embodiment is Avalokiteshvara — the bodhisattva of compassion, who hears the cries of the world.
Karuna is trained, not assumed. Tonglen is its most direct practice.