The physical heart is the physical manifestation of the Anahata Chakra or the center of the Chalice - the heart of the Subtle Body.
Surya-Vidya - thus was the Teaching of the Heart sometimes called. In this definition was indicated the fieriness, the sunlike quality, the centrality of the heart. Verily, anyone who wishes to cognize the heart cannot approach it as only a part of the organism. First of all, one should recognize the centrifugal aspect of the heart and study outward from it, not inward toward it. The solar plexus is the antechamber of the temple of the heart. The Kundalini is the laboratory of the heart. The brain and all the centers are the estates of the heart, because nothing can exist without the heart. Even the brain can be supplemented to a certain degree. Even the Kundalini can be somewhat nourished by a manifestation of electricity, and the solar plexus can be strengthened by blue light. But the heart stands as the temple of humanity. One cannot conceive of the unity of humanity by way of the brain or the Kundalini, but the radiance of the heart can bring together the most seemingly varied organisms, even across remote distances. This experiment, of the unification of hearts across distance, awaits its workers. (H, 339)
The heart in its full significance is a transmuter and a condenser. Often these processes happen to be so strong that human strength cannot suffice to contain and endure the tension. From antiquity has come the prayer about resigning one’s spirit to God. One should understand truly this surrender of the spirit. If you feel an unbearable anguish of the heart, transfer it mentally to the Lord. Thus you may join your heart with the Inexhaustible Source - Hierarchy. Such action may be particularly needed when the tension of the entire planet is great. One must be prepared for the most diversified influences, both cosmic and human. The adherence of the heart to Hierarchy is a continuous action, but at present We are pointing out particular instances when it becomes necessary to strengthen the heart with the manifestation of Hierarchy with especial clarity of consciousness. Many will not understand how one can strengthen the heart by thought, because for them the heart is but a physical organ. But whoever has felt Our currents will understand the meaning of this bond. The World is living through such a tension that it is timely to remind about the necessity of readiness for such communions. The Fiery World must be evoked in full consciousness. In case of need one may even orally address the Lord. Upon all steps of Hierarchy there is the same transmission and communion. And how majestic is this Ladder of Immeasurable Help. (FW II, 94)
Lacking straight-knowledge, who can imagine the reality of the Fiery World? But this quality must be cultivated with all devotion; and this devotion must be precisely in the heart, not on paper. Also, acceptance of the Fiery World proves courage, for any ignorant thought primarily rebels against the fires of the heart. (FW I, 209)
A hardened heart will not ascend to the Tower. It will not give strength to the subtle body. Such a stony heart will remain within the confines of Earth.
(BR, 113)
Not many realize that the development of the heart means, first of all, the broadening of the consciousness. Verily, the heart is the throne of the consciousness, but not sentimentality, this surrogate of benevolence. (LHR I, p 397)
The cry of the heart is generally understood as an abstract concept, but Ur. says not so, for she has known and heard the resounding of the heart in its great tension. Such sounding actually occurs, and in it is expressed a powerful energy. The most dangerous assaults of darkness are shattered against this tension of energy. But not often is it possible to attain such a striking aspiratory state. The fiery heart knows when the invocation of the entire psychic energy will be demanded. From the solar plexus, from the chalice, there is concentrated a current of powerful force. The most evil sendings will fall apart under such a discharge. We always rejoice at seeing such a vigilant heart, since the attack is always sudden and the accumulation of force is only possible through great watchfulness. Often this keen vigilance becomes clouded by a kind of faintness which is very indicative of the presence of dark forces. But a flaming heart does not give in to such poisonous chemisms. But remember that evil forces do send double, repeated blows, knowing their effect upon unprepared organisms.
(FW II, 169)
It is asked - What center is particularly important just now? The present is a time of synthesis, therefore let us begin everything from the heart itself. Precisely the heart stands above all. Therefore, let the throat and the chalice and the solar plexus not be isolated from the guidance of the heart. (FW II, 210)
The heart is the highest manifestation of the sixth principle. The heart is the abode of Brahma. (LHR I, p 323)
see also Chakra, Chalice, Image in the Heart, Kundalini

This definition is in context to Classic Yoga. See more contextual defintions for Heart.