What is Rosh Hashana?
Rosh Hashana is the day on which G-d completed the creation of this world, by creating Adam, the original man. Adam's very first act was to proclaim the Almighty as King of the Universe. He called upon all creatures: "Come, let us worship, bow down, and kneel before G-d, our maker."
Each Rosh Hashana, we too proclaim the Kingship of G-d, and reaffirm our commitment to serve Him well.
Just as on the original Rosh Hashana, G-d created the world for the first time, so each Rosh Hashana He reconsiders and re-evaluates the quality of our relationship with Him, and creates our world anew.
The Book of Life
On the first evening of Rosh Hashana, after services, we exchange the traditional blessing, "May you be inscribed and sealed for a good year."
Our sages explain that on Rosh Hashana, we all stand in judgment before G-d -- "like a flock of sheep before the shepherd." If we are worthy, we are "inscribed" in the "Book of Life." Ten days later, on Yom Kippur, the Book is sealed.
Through repentance, prayer, and charity, we can sweeten the decree, and merit G-d's blessings for health, wellbeing, and prosperity for the coming year.
Please read the Essays for more insights on the above points.