Following the crowning of God as king on Rosh HaShana, His kingship is expressed on Yom Kippur by His absolving our sins. God is the King of the Universe, and accordingly, He removes us from our slavery to the evil inclination, and brings us into His domain.

Entering the domain of the King of the Universe:

An aspect of Yom Kippur is…that the world is the King’s, God’s, just like a servant belongs to his master. Consequently, the Holy One, blessed be He, absolves their sins, because they [the Jewish people, or perhaps mankind] are His…and from the fact that He is the King of the Universe, and everything in it is His, under His domain and no one else’s. So on Yom Kippur they emerge from the domain of that king, the evil inclination, with whom they became entangled during the year, and they enter the domain of the Holy One, blessed be He, because they are called by the name of the King, the Lord of hosts…. The sinner is sold into the hand of the evil inclination through his sins, until he is able to come under the domain of another; and on Yom Kippur, he emerges [from the domain of the evil inclination]. (Maharal, Gevurot Hashem 46)

Further reading: With regard to the Kaparot ceremony that takes place before Yom Kippur, see A Concise Guide to Halakha, p. 158.