God said, “Let there be lights in the dome of the sky to divide the day from the night; let them be for signs, seasons, days and years; and let them be for lights in the dome of the sky to give light to the earth”; and that is how it was. God made the two great lights — the larger light to rule the day and the smaller light to rule the night — and the stars. God put them in the dome of the sky to give light to the earth, 18 to rule over the day and over the night, and to divide the light from the darkness; and God saw that it was good. ~ Genesis 1:14-18
In Hebraic tradition, there is a strange tension and rivalry between the “two great luminaries,” the sun and the moon. While both mark time through their cycles, they are very different. In terms of seasons and the natural world, the start of each year is practically the same. With each month, however, there is a dramatic transformation from its beginning to its end.
The Hebrew words for years and months reflect this difference. In Hebrew, a year is called a shanah, which comes from a root meaning “to repeat.” A month is called a chodesh, which means “to become new.”
Thus, every month is an opportunity for renewal - renewal of commitment to God's laws and principles, renewal of surrender to God's will, renewal of repentance and turning from our opportunities for sin and compromise, renewal of unity with our brothers and sisters.
The monthly prayer dedicated to the new cycle of the moon has nothing to do with the moon itself, it is not the focus of worship in any way. It is not the moon that is blessed, but God who is praised for creating the cycles that renew the moon, with the following prayer:
Praised are you, O Lord our God, King of the Universe, who created the skies with his word, and all heaven’s host with the breath of his mouth. He gave them appointed times and roles, and they never miss their cues, doing their Creator’s bidding with gladness and joy. He is the true creator who acts faithfully, and he has told the moon to renew itself. It is a beautiful crown for the people carried by God from birth, who will likewise be renewed in the future in order to proclaim the beauty of their Creator for His glorious majesty. Praised are you, O Lord, who renews new moons.