The Mishna in Yoma 8 states, "Sins that are between a person and his friend are not atoned for on Yom Kipur." One cannot offend and harm another person and ask for forgiveness from G-d. Forgiveness must be asked and can only come from the person that we hurt, and only he can pardon us.
Thus, on the morning of Yom Kipur we read the amazing words of the prophet, Yeshayahu, (Ch.58) where he presents a debate that takes place between G-d and Israel. In this chapter, we see how Yom Kipur can lead us to change our evil ways and be just and compassionate to our fellow Jew.
Yeshayahu states that Israel claims before G-d, (Ibid.) "Why have we fasted and You (G-d) did not pay attention; we have afflicted our soul, and You (G-d) do not know?"
This question is asked after the Yom Kipur fast, when G-d's pardon is not apparent. The people cry out, "Why hasn't the Yom Kipur fast helped to obtain forgiveness?"
G-d's response is clear and unequivocal – "Will such be the fast that I will choose, a day of a person afflicting his soul? Is it to spread out sackcloth and ashes? Will you call this a fast that is acceptable to G-d? Do you (human beings) think that I desire you to suffer? Do I get any benefit from the fact that you afflict yourselves?"(Yeshayahu 58).
G-d is telling us that the Yom Kipur fast is not only an end in itself but the means to reach a further goal. What is this yearned for goal? G-d responds to this question with the surprising answer, "Is this not the fast I will choose? Is it not to share your food with the hungry and to bring the poor into your home, when you see a naked one, you shall clothe him and not hide from your fellow Jew." (Ibid.)
Here G-d explains the goal that He wants our Yom Kipur fast to achieve. The purpose of the fast is not to suffer or to diet. The purpose is that we should remember the poor, those who do not have proper food, clothing or shelter. This is the true purpose of the Yom Kipur fast.
Thus, Yeshayahu promises, "Then you shall call, and G-d shall answer; you shall cry out, and He shall say, 'Here I am'."
Therefore, on Yom Kipur we repeat over and over again the 13 Attributes of G-d's Compassion, "G-d, G-d, Compassionate and Gracious, Slow to Anger and Abundant in Loving-kindness and Truth…, Forgiving iniquity, rebellion and sin." (Shemot 34).
Why do we keep repeating these verses over and over again on Yom Kipur? When we repeat this declaration again and again, we become convinced that the correct path between us and our fellow Jew is G-d's path of compassion, forgiveness and loving kindness. We turn to G-d in the merit of those very same qualities with which He identifies Himself, and thus we awaken those same traits in ourselves.
As the Talmud in Rosh Hashana states, "Whoever forgives his friend for sinning against him even when he doesn't have to guarantees similar treatment from G-d on Yom Kipur." If we make a habit of displaying undeserved grace to others, including those who have committed wrongs against us, then we are guaranteed to earn the same kind of undeserved grace from G-d MIDAH K'NEGED MIDAH. G-d conducts Himself with us in the same way that we conduct ourselves with our fellow human beings.