The consciousness to which the body mind appears is that limited, does that grow old? Does that grow through ups and downs? Unhappiness and frustration? No. Not as a matter of stipulation, not as a rhetoric, but I come to see that it is so. That is Brahman. And if you realize that this very Atman, the Self as Brahman, is, he says, Amrita Abhavanti,. You become immortal, become immortal figuratively only. The next two verses are teachings of meditation, yogic meditation, in order to attain this realization.
Swami Sarvapriyananda teaches the Katha Upanishad, one of India's most revered texts which is also a part of the Vedas. It is a collection of philosophical poems representing a conversation between the sage Naciketas and Yama (god of death). They discuss the nature of Atman, Brahman and Moksha(liberation).