Rosh HaShanah is the day on which G-d created Man, Adam, G-ds final and most precious creation. Each Rosh HaShanah, the birthday of Mankind, we proclaim G-d as our one and true King. We then reaffirm our desire to serve him every moment of our lives. At this same time, G-d reviews the status of his creation and determines if he or she merits another year in this world.
On the first night of Rosh HaShanah, after prayer services, a special greeting is used, which is only said on this night "May you be inscribed and sealed for a good year." On Rosh HaShanah, everyone is judged by G-d based on his or her actions during the previous year. The resulting judgment is inscribed by G-d and a persons future is determined for the following year. Though that judgment is inscribed, it is not yet sealed and can still be changed at least for another ten days. G-d waits until Yom Kippur to seal the book for the year.
How can a person change their judgment for the better? "Repentance, Prayer, and Charity can remove the bad decree." G-d looks especially at three areas during the time between Rosh HaShanah and Yom Kippur, the Ten Days of Repentance. By doing teshuvah with true regret for the past and commitment for the future, a person can erase his misdeeds and hence improve his judgment before it is sealed on Yom Kippur. Similarly, by praying with greater concentration before G-d, and by giving charity with the proper spirit, one can also upgrade one's status.