The following is an excerpt from a letter written by Rav Wolbe (Iggros U'Kesavim vol. II p. 158) to his "dearest loved ones."
The Ramban writes (Vayikra 23:24) that Rosh Hashana can be described as a yom din b'rachamim - predominately a day of strict judgment, yet Hashem adds a measure of compassion to the judgment. In contrast, Yom Kippur is a yom rachamim b'din - a day of abundant compassion notwithstanding the judgment which also takes place. Additionally, by means of the five restrictions of the day, Hashem elevates us to otherworldly levels. Chazal tell us regarding Olam Haba (Brachos 17a), "There is no food, drink, procreation...jealousy, hatred or competition...the righteous sit...and enjoy the radiance of the Shechina;" an apt description for Yom Kippur.
Just as the day is overflowing with Heavenly compassion and love, similarly, Klal Yisrael must act with compassion and love toward one another. Accordingly, Chazal tell us that a lack of love can have serious repercussions, for Yom Kippur does not atone for sins between man and his fellow man unless the offended party is appeased (Yoma 85b). Thus, the most essential preparation for this holy day is for people to forgive and appease each other, and the more one does in this area the more praiseworthy he is. Therefore, I am asking of you: On Erev Yom Kippur please call to wish each other a good and sweet year, appease each other and sincerely forgive each other.
Yes, I know that sometimes a person has feelings of anger bottled up inside himself. The way to quell these feelings and overcome the anger is by arousing feelings of compassion toward the other party - see what I have written in Alei Shur vol. II p. 221. After all, as mentioned, this is the avodah of the day: to arouse feelings of love and compassion toward our fellow man. Moreover, Chazal tell us that Heaven will act compassionately toward one who has compassion on his fellow man - and who does not need a big dose of Heavenly compassion?!
Hence, please prepare for this tremendous avodah which is much greater and more important than searching for white chickens for kaparos and the like. Furthermore, hurry to carry out this endeavor and don't wait for the other party to call you. Rather, you should be the first one to pick up the phone to call. Don't make calculations such as, "I am angry at him, why should I be the one to initiate?" Many have the custom of learning the sefer Orchos Chaim L'HaRosh during these days and he writes (Siman 61), "Do not hold your anger against a fellow Jew for an entire day. Bend over toward him and be the first one to ask for forgiveness." Similarly, Rabbeinu Yonah writes, "Even if he has sinned toward you, you should go to him to obtain appeasement and don't say, 'He wronged me, he should initiate the appeasement.' Rather subdue your yetzer and go over to him" (Sefer Hayirah 175).
Everyone is in need of Heavenly mercy during these Days of Awe, whether it be in the area of health, livelihood, children or any other spiritual or material lacking. What I have written is a wonderful way to arouse mercy upon oneself and his family: be compassionate and merciful toward another person, and run to be the one to appease and make amends. The timing is especially significant, because in light of the seriousness of these days, one often finds that he might not have been as right as he thought he was when the incident occurred in the middle of the year.
My dearest loved ones, I am guaranteeing you that if you follow my instructions you will b'ezras Hashem have a feeling of utmost pleasantness on this Holy Day which is approaching. However, Chazal guarantee that if you follow these instructions, Heaven will have mercy upon you!
May you all be blessed with a sweet year and a bounty of success in body and soul!