Rosh Hashanah includes three stages of divine service, expressing three levels of attachment to G-d.
1) The bond created by doing mitzvot. A Jew is, so to speak, an existence separate from G-d, and fulfillment of mitzvot is what forms and creates the bond between them. This bond is expressed in the mitzvah of the day -- blowing the shofar.
2) An inner bond, not dependent on mitzvot. This level is expressed in repentance: even a sinner feels regret and repents. However, even this level, which transcends the bond created by mitzvot, is nevertheless connected to them. A person regrets lapses in mitzvah observance, and resolves to correct precisely that. Since this resolve is linked to mitzvot, it involves a person, a separate existence, bonding to G-d through mitzvot.
3) The Zohar states that “The Jewish people and G-d are entirely one”, i.e. that a Jew and G-d are essentially the same entity, so to speak. This level of unity is expressed through the coronaiton of G-d. The bond through mitzvot and the one through repentance are only created after the coronation. Only then is general obedience to the King possible (and repentance for its absence). However, before the coronation (before the service of “Proclaim me a King over you”), what brings a Jew to feel the need for G-d’s Kingship, so that he asks G-d to accept the coronation and accept him as a servant? The answer is that a Jew is in essence one with the Creator, and so he cannot be without his King.
(Likkutei Sichot, vol. 19, p. 350)
