Why do we celebrate Rosh Hashanah?
Rosh Hashanah is far more than the non-Jewish concept of the New Year.
As the first day of the year, Rosh Hashanah is a day of judgment: it is the day upon which the matters of the coming year are decided, and therefore it is one of the most central days of the Jewish calendar.
On the other hand, the day of Rosh Hashanah, on which Hashem judges us, is a day of coronation for Hashem: We enthrone Him, so to speak, as judge upon the entire world, and with this itself we merit a positive judgment.
Therefore, the basic motif of the day is the coronation of Hashem, whereas the judgment that takes place on the day sets the background for the ceremonies and prayer service of the time.