From the Taittirīya Upaniṣad: five layers or sheaths within which the self appears to be enclosed. Each layer is subtler than the previous. Ātman is what remains when all five are recognised as not-self.
The Taittirīya Upaniṣad describes the self as appearing to be contained within five sheaths (kośa = sheath, like the casing of a sword). Each sheath is a layer of identity that the uninformed person mistakes for the self. Moving inward from coarsest to subtlest:
The point of the model is not anatomical. It is discriminative: at each layer, the Upaniṣad asks — is this the self? No. Is this the self? No. The self is what is known, not the knower of the known. It is what witnesses the body, the breath, the thoughts, the intellect, the bliss — without being any of them.
The Taittirīya Upaniṣad's second chapter (Brahmānandavallī) proceeds through the five kośas in sequence, describing each as a self (ātman): the inner self is filled with prāṇa, filled with mind, filled with vijñāna, filled with ānanda. Each is called ātman provisionally — to lead the student inward. The structure is not five separate substances nested like Russian dolls. Each inner kośa is the ātman of the outer — the life-force is what animates the food-body; the mind is what directs the life-force; the intellect discriminates among the mind's contents; the bliss-body is the deepest rest. And Ātman itself is what is aware of all five.
Śaṅkara uses the Pañcakośa model as a systematic practice of neti-neti — the via negativa applied to the layers of identification. For each sheath: I am not this body (observed, objectified, changed). I am not this breath (it comes and goes). I am not these thoughts (they arise and subside). I am not this intellect (it is an instrument). I am not even this bliss-body (it is present in deep sleep but absent in other states). What remains — the witness of all five states — is Ātman. The model does not add anything to the recognition of Ātman. It systematically removes the false identifications that obscure it.
The status of the ānandamaya kośa generates significant debate in the Advaita commentarial tradition. The Taittirīya seems to identify it as Brahman in some passages (ānandaṃ brahmeti vyajānāt — he knew bliss as Brahman, Taittirīya 3.6.1). Śaṅkara's resolution: the ānandamaya kośa is not Brahman but the closest kośa to Brahman — it is Brahman's reflection in the causal body, the deepest conditioning layer. It is not Ātman itself because it appears only in deep sleep and in deep absorption, not in all three states. The witness of deep sleep (the one who says "I slept well") is Ātman; the bliss experienced in deep sleep is the ānandamaya kośa. This distinction is technically important: confusing the ānandamaya kośa with Ātman would locate the self in a particular experiential state (bliss) rather than in the witness of all states.
The Pañcakośa model and the Māṇḍūkya's four-state model (waking, dream, deep sleep, Turīya) map onto each other partially but not precisely. The three gross kośas (annamaya, prāṇamaya, manomaya) are primarily operative in the waking state. The vijñānamaya kośa is the subtle body that persists through waking and dream. The ānandamaya kośa is the causal body of deep sleep. Turīya is the witness of all three states — corresponding to Ātman as distinguished from all five kośas. Together the two models provide a comprehensive account of the self from the directions of structural layers (Pañcakośa) and temporal states (Māṇḍūkya). Advaita uses both frameworks as complementary approaches to the same non-dual recognition.