Sri Aurobindo translates Katha Upanishad, Second Cycle: Second Chapter, Verses 4-6: “When this encased Spirit that is in the body, falls away from it, when He is freed from its casing, what is there then that remains? This is That thou seekest. Man that is mortal lives not by the breath, no, nor by the lower breath; but by something else we live in which both these have their being. Surely, O Gautama, I will tell thee of this secret and eternal Brahman and likewise what becomes of the soul when one dies.”
The mystery of life and death is explored in detail starting with these verses. When an individual is born, what is it that signifies life in the body? When an individual dies, what is it that departs to signify the death. The most obvious physical sign is the departure of the breaths, inhalation and exhalation being the primary observable breaths (prana and apana in the Sanskrit). Without the breath of life, the body begins to decompose and decay, “dust to dust” as the Christian burial eulogy goes. But the breath alone does not bring with it automatically those things which we associate with intelligent life. The breath can be functional without there being any active mental process of perception, will, memory, imagination, analysis or synthesis, or logic and reason. When the breath departs, it is true, that these higher functions also depart. The Upanishads evaluated causation and primacy and determined that the body itself, as well as the life-breath, were not primary causative factors, rather they were instruments utilized by some other factor. Further analysis yielded the understanding that the mental process is also contingent on something further. Eventually they came to appreciate that there is a “first cause”, which they called Brahman, which creates all life and infuses it with awareness and purpose, and which is itself the container and the substance of the creation.. The spark of the Brahman that activates what we recognise as the human being was called the Atman or as we may call it, the soul.
From this viewpoint, it is the Atman which, when it enters into the physical form, provides awareness and life energy, harnessing the prana or life-breaths to carry out the actions of life. When the Atman departs, the machinery of the physical body infused with life-energy ceases and the physical body breaks down into its constituent elements.
The Atman, being a spark of the awareness of the Brahman, does not die with the death of the body. It should be noted that some believe that the Atman is not a particular formed individuality, but a stream of conscious energy that continues and takes new forms as it evolves. Either way, it is the Brahman which supplies the continuity throughout the process of birth, life and death, and the recurrence of the pattern.
Sri Aurobindo, The Upanishads, Katha Upanishad, pp. 213-241, and Kapali Sastry, Lights on the Upanishads, pp. 104-129