The significance of the Kaushitaki Upanishad is not easy to understand. There are at least two important themes: the transmigration of souls and an attempted determination of Brahma. The first theme is interlaced with passages remarking on consequences of moral (usually sacrificial) actions. It is in these passages that one can find expressions of the famous doctrine of karma. Interestingly, the transmigration of souls from one life to the next includes passage of the soul to the sun and then to the moon before returning to its next incarnation.
One is reminded of Plato's description of reincarnation in the Myth of Er where souls are allowed to choose their next existence, but their choices are usually determined by what they did or experienced in their previous existence. Furthermore, if one had been dedicated to sound philosophy in one's previous life, one had a better chance at making an auspicious choice. The parallel with the transmigration of souls as expressed in the Kaushitaki Upanishad lies in the karmic consequences of one's actions and the soul's ability to escape these consequences through a proper understanding of Brahman.
The determination of Brahma is expressed in a dialog between a brahman named Balaki and a kshatriya named Ajatasatru. Balaki begins by attempting to explain the nature of Brahma, but after each attempt, Ajatasatru refutes him. Humbled, Balaki presents himself to Ajatastru as a pupil; whereupon Ajatastru reveals the truth to Balaki, explaining that Brahma is the Atman (or the soul with us) that is "minute as a hair subdivided a thousandfold" and which when awakened is like a blazing fire sending sparks in all directions. The force of this metaphor is that the Atman is Brahman, but that the individual soul is to Brahman as sparks are to a blazing inferno.
While not the most fascinating of the Upanishads, the Kaushitaki Upanishad's themes are unquestionably among the most important in the canon.