"Hridaya Tvam Asi: The Heart You Art!" means that the Heart, thus, is Tat.
From the Sri Lalita Sahasranama:
425.Tat Tvam Asi: That You Art!
She who is meant by "That," the Supreme Truth, Brahman
When knowledge of Brahman arises in the intellect, Tat (that) is the word used to signify that Brahman (See mantra 363).
Tat is a pronoun - a word which is employed to refer to something that is already indicated. All known things are included in tat because behind everything is Devii, the Supreme Consciousness.
In the naamaavali form of the Sahasranaama in which Devii is invoked name by name, this mantra becomes Om Tasmai Namah. Tasmai is the dative form of the pronoun Tat.
In Jivanta, Tat Tvam Asi -- That Thou Art! -- refers to the Heart, to the Mother. Idam Tvam Asi -- This Thou Art! -- refers to the Beloved, the Father