In the Jewish tradition, the days following Rosh Hashanah are a progression toward Yom Kippur, the Day of Atonement. Atonement is more than simply offering an apology, it is actively working to make right a wrong you have committed, and toward restoration of the relationship with the person or persons against whom you have transgressed.
Similarly, in Twelve Step programs, there is emphasis on not merely expressing regret, but doing everything you can to make amends to those who have been wronged by your past actions. Regardless of whether the person to whom you are making amends is able to forgive you, there is tremendous spiritual benefit in taking action toward the healing of the relationship.
Being genuinely regretful addresses your commitment to Spirit (both Holy and personal), while engaging in actual effort to right your wrongs and repair your ruptured relationships addresses your commitment to people.
On the flip side, there is forgiveness. Forgiveness does not require that you absolve someone of responsibility for their wrongdoing. Forgiveness is a release – for yourself – from the burden of anger and bitterness. Forgiveness says, “I am no longer imprisoned by my perception of your offenses.”
Seeking forgiveness is not necessarily a straight path. Granting forgiveness is rarely a direct route. Each can be a labyrinthine journey of twisting pathways and feeling as though you are traveling backward in order to progress. But reaching the center – making peace (with yourself, with others, and with the Divine) – is well worth the long walk on the winding path.