The Jewish nation mourned for thirty days following the passing of Moses. (During this time, Joshua, the new leader of the Jewish nation, sent scouts to spy on the land of Canaan, see Jewish History for the 5th of Nissan).
On the 7th of Nissan, the first day after the mourning period came to an end, Joshua instructed the Jews to stock up on provisions and prepare themselves to cross the Jordan river and begin the conquest of the Promised Land. This was the first time Joshua addressed the nation, and they unconditionally accepted him as their new leader.
Once a month, as the moon waxes in the sky, we recite a special blessing called Kiddush Levanah, "the sanctification of the moon," praising the Creator for His wondrous work we call astronomy.
Kiddush Levanah is recited after nightfall, usually on Saturday night. The blessing is concluded with songs and dancing, because our nation is likened to the moon—as it waxes and wanes, so have we throughout history. When we bless the moon, we renew our trust that very soon, the light of G‑d's presence will fill all the earth and our people will be redeemed from exile.
Though Kiddush Levanah can be recited as early as three days after the moon's rebirth, the kabbalah tells us it is best to wait a full week, till the seventh of the month. Once 15 days have passed, the moon begins to wane once more and the season for saying the blessing has passed.