Interestingly, the words Rosh Hashanah " do not appear in the Chumash. Rather, Bemidbar 29:1 refers to Yom Teruah, a day of blowing of the horn. The closest we come to Rosh Hashanah is in Devarim 11:12: A land which the Lord your God cares for; always are the eyes of the Lord upon it, from the beginning of the year (me-reshit hashanah) until the end of the year. The context in which these words appear is significant: Gods love and concern for Eretz Yisrael.
Question: Why doesn t the Torah simply state that Gds eyes are always on the land? Why does it add the phrase, From the beginning of the year to the end of the year?
Perhaps the Torah is informing us that Gd's concern for the Land is not automatic. It is renewable at every beginning of the year. But we must earn that renewal. And it is renewed at Rosh Hashanah because this is when we renew our own relationship with God, crowning Him as our King. When we do this, we effect a reaction in heaven. God reciprocates and renews His love for us, once again focusing "His eyes on His land.
May we be worthy of renewing our attachment to Him this "Reishit Hashanah," and may He once again renew His divine care and deliverance.
Shanah Tovah!