The days from Rosh HaShanah until Yom Kippur are called Aseret Y'mei Teshuvah, the Ten Days of Repentance. During this period, our relationship with God changes, as reflected in two changes in the daily prayers: instead of "the Holy God," we say "the Holy King"; and instead of "the King Who loves kindness and justice," we say, "the King of justice."

What is the significance of these changes?

Divine Rule
God governs the world in a different fashion during the Ten Days of Teshuvah. During the the year, His rule is revealed through the attribute of Elokut (Godliness); but during this special time, He rules with the attribute of Malchut (Kingship). What does this mean?

A king judges his subjects according to their current state, deciding who deserves punishment and who deserves reward. In the Divine rule of Malchut, evil is not tolerated.
God permits evil so that the wicked will have the opportunity to repair their evil.

In the elevated Divine view of Elokut, on the other hand, everything has an ultimate purpose. God's praise, the sages taught, also comes from the wicked (Shemot Rabbah 7). It may be beyond our limited understanding, but also evil serves a purpose in the world. Ultimately, the wicked through their free will only bring sorrow upon themselves.

During the rest of the year, God permits evil so that the wicked will have the opportunity to repair their evil during the Ten Days of Teshuvah. We refer to God during the year as the "Holy God," since even base and wicked actions will lead to holy goals. This form of Divine rule emphasizes God's kindness and forbearance, and our prayers speak of God as "loving justice and kindness."

During the Ten Days of Teshuvah, however, God is revealed as the "Holy King." The time has arrived for the wicked to mend their ways. If they fail to repent, they will be dealt with the attribute of mishpat, exacting judgment. During these ten days we experience God's providence as a King who rejects all evil, and thus refer to Him as "the King of judgment."

[Adapted from Olat Re'iyah vol. I pp. 272-273]