From the Rebbe’s explanations:
– The full shining of the moon on the fifteenth of the month reflects a level of perfection in regard to its power of revelation. However, the essence of the moon, its very being, is reflected in its rebirth in the beginning of the month [but not in the state of the full moon].
Since the time of Geulah relates to the essence of the Jewish people, it is symbolized by the rebirth of the moon. The uniqueness of Geulah, is that in that age, the essence will come into revelation; the essential qualities of the Jewish people will be openly apparent. Our essential bond with G‑d will permeate every aspect of our conscious functioning, to the extent that it is reflected in our thought, speech, and deed.
Based on the Rebbe’s talk on chapter Toldot (5752).