The goal of Yom Kippur is that we successfully clean our slate both in connection with laws between man and G-d, as well as those laws that are between man and man.
According to the Rambam, the essence of Teshuva is Viduy, or confession. Verbally expressing our remorse for our actions is a major step towards achieving atonement. It takes a great deal of humility to have the courage to say the words, “I was wrong.”
It is probably more difficult to say those words to another human being than it is to say it directly to G-d. It is less formal than having to swallow our pride and own up to our bad behavior.
The hope is that we give our interpersonal relationships a good, hard look. It is never too late to ask another person for forgiveness, even if many years have passed.
We need to enter Yom Kippur being at peace that we made things right in all of our interactions with others. It is only then that we are able to face our Creator with a clear conscience, so that we are worthy of His forgiveness.
What might be most important of all is that we do not hold a grudge against those who have wronged us. We should also pray for those who are unable or unwilling to make amends, and hope that one day, they, too will do a sincere Teshuva.
It is not an easy task before us, but we are grateful for this day of Yom Kippur where we have the possibility of making things right, between man and man, and man and G-d.