One-heart is our English word for compassion, the Sanskrit karuṇā. The name emphasises the oneness of all things: that our suffering and pleasure are interconnected, that we are, at root, one being seeing itself through many eyes. One-heart is empathy grounded in this recognition.
But one-heart is not merely kindness, and it is not the same as being pleasant or agreeable. In Tianmu, true compassion is the action that brings someone closer to enlightenment. It is the desire to free every being from ignorance and to show it its own true nature, its own divine nature and its free will. A compassionate act may be gentle or it may be fierce; what defines it is not its tone but its direction. If it moves a being closer to waking up, it is one-heart.
This understanding is shared with the Mahayana Buddhist tradition, where the bodhisattva's compassion is not passive sympathy but active liberation, the commitment to work for the awakening of all sentient beings, by whatever means are necessary. One-heart is, in this sense, the emotional complement to Skillful Means: skillful means finds the door, and one-heart is the reason you knock on it.