The beautiful Sanskrit word 'Kshama' is usually used as the equivalent to 'forgiveness'
As is with most translations, this too limits the depth of the meaning. Kshama is much more than just saying 'I am sorry'.
Kshama comes from the Sanskrit root verb 'ksham' and has several meanings; patience, forbearance, pardon. Root meanings of the word kshama also includes 'to release the grip, to let go, and to lift up' -- letting go of our attachment to a grievance with another. It also means to have capacity to be 'large hearted', to have the ability to absorb and dissolve all assaults, the ability to accept the validity of diverse points of view.
Kshama has a quality of spacious equanimity and the promise of compassion. It is restraining intolerance with people and impatience with circumstances and implies remaining serene, patient and observing self-restraint, doing good to all, even to those who may want to harm you.
Another interpretation offered by the wise is -- Kshama consists of ksa meaning to destroy and ma meaning to protect i.e. ksama means to protect from destroying the nature or virtues of soul. And this bears the closest semblance to the Jain meaning of forgiveness...
It's important however, to remember that forgiveness doesn’t excuse the behavior that caused your hurt. Forgiveness prevents the behavior from destroying your heart. When you forgive someone who has wronged you, you take away the power of the hurt. Only then can you begin to heal. Only then is your heart free enough to take on the healing process. If you continue to be hurt, healing cannot begin.
If you are the one seeking forgiveness, it is often hard to muster up the courage to say you’re sorry. And then it can be even harder when someone doesn’t accept your apology. But that’s ok. People are allowed to not accept your apology or need some time and space to think on it. You cannot control what they say or do, but you can control what you say and do. So stay steady and calm, manage your emotions of rejection and hurt, and show your apology through consistent actions -- demonstration.
I know as a child I was taught that once you realised you had hurt or upset someone (intentional or otherwise), you should move quickly to correct that, apologise -- set things right. In my grandmother explaining this, it also involved a discussion about sincerity, which is often part of the challenge of an 'I'm sorry' being genuinely heard or received -- incongruence in the energy between saying and meaning. Each of us has our own challenges on either end of the process, and taking responsibility for our thoughts, speech and actions is a foundational aspect of living our yoga off the mat. I'm a big fan of the 'pause', though sadly being human at times I fail, falling into reactionary mode when triggered, particularly if emotionally invested or tired. Mmm, Viveka, Vairagya -- more on these other important Sanskrit terms later.
Some other things to consider...
'..forgiveness is really not for the other person’s benefit at all -- it’s for our own. Regardless of how illogical it may seem at times, it is through unconditional forgiveness that we surrender the past to the past and enter the present, freeing ourselves to stand in the infinite Light that knows how to heal our deepest and most painful wounds.' Dennis Merritt Jones
The ho’oponopono prayer goes like this: 'I’m sorry, Please forgive me, Thank you, I love you.'
At any time we can ask ourselves, 'what would love do?' it's a beautiful space from which to consider any actions.