As pure water poured into the pure becomes of the same quality, thus, oh Gautama, the Ātman of the sage who knows becomes [pure].

This verse describes the transformation of the Ātman through knowledge.

Yathodakaṃ śuddhe śuddham āsiktam — as pure water into the pure. The example of undifferentiated union.

Tādṛg eva bhavati — becomes of the same quality. Complete identification.

Evaṃ munervijānataḥ — thus of the sage who knows. Muni = the silent one, the contemplative.

Ātmā bhavati gautama — the Ātman becomes, oh Gautama. Naciketas is called Gautama.

The verse indicates that the individual Ātman, when purified by knowledge, reveals itself as the supreme Brahman. There is no real transformation of the Ātman — it is always pure — but the appearance of impurity is dissolved.