Meaning and elaboration
Meaning: The Manifest and Unmanifest Form of the Self.
Elaboration
Vyakt'avyakt'atmika Murti names Mahakali as the form of the Self that is at once manifest and unmanifest. She is the universe that can be seen, known, and experienced, and she is also the transcendent reality that the senses can never fully grasp.
The Manifest (Vyakta) "Vyakta" refers to what is manifest, discernible, and available to the senses and intellect. In this aspect, Mahakali is the whole cosmos in its diversity: all forms, names, phenomena, and beings that make up creation. She is the Shakti expressing itself as the five elements, the planets, the stars, the mountains, the rivers, and all living creatures. Here she is the visible and lived reality, present in every atom and every being.
The Unmanifest (Avyakta) "Avyakta" refers to what is unmanifest, beyond the reach of the senses, and inaccessible to the ordinary mind. This is Mahakali as the primordial, formless ground of existence, the transcendent Void (Shunya) or the absolute Brahman. It is the state before creation, during dissolution, and beyond conceptual thought. This is her timeless and unconditioned essence, the source of all manifestation that remains untouched by what it brings forth.
The Self (Atmika Murti) "Atmika Murti" means "the form of the Self." Here the Self refers to the Universal Self, Brahman or Paramatma, the ultimate reality that is the essence of all beings and of the cosmos itself. To say that Mahakali is this form, both manifest and unmanifest, is to affirm that she is the foundational non-dual reality, the Advaita Tattva, from which everything arises and into which everything dissolves. She is the consciousness that pervades all and yet transcends all.
Bridging the Dualities This name bridges the apparent divide between the personal God with form (saguna Brahman) and the impersonal, formless absolute (nirguna Brahman). As Vyakt'avyakt'atmika Murti, Mahakali is the power through which the transcendent unmanifest becomes the immanent manifest without ever ceasing to be transcendent. For the devotee, this means that the Mother worshipped in her fierce, dark forms is none other than the formless Self abiding at the core of one's own being and of the entire universe.