Because of the importance of the day, the entire month of Elul preceding Rosh Hashana is a month of introspection when we prepare ourselves.
During Elul, we ask forgiveness of people who we may have hurt, we look at our growth over the previous year and see where we could come closer. Primarily during the month of Elul, we recognize and prepare ourselves to crown the Creator as King, Melech. When we take the crown off of our own heads (e.g. our ego-wants) and place it on the Creator's head (for the sake of His Will), we properly prepare ourselves spiritually by once again remembering and confirming that there is a Supreme Being who is in control of our destiny and the entire world.
We ask on Rosh Hashana to be inscribed for a sweet year, full of blessings of health and prosperity, love and success.
By properly preparing ourselves, we cleanse ourselves before that day and "pay our debts" for errors and mistakes made the previous year, so that we stand before the King and can receive a sweet year.