To let go of.. whatever entanglements between a wrong doing, mostly.
Depending on the nature of the relationship between parties involved.
If there's an ongoing relationship or forced proximity between the parties involved, forgiveness would result a less awkward, less discomfort or tension in whatever they had to do that made them not avoid another else's presence.
Or that the need for forgiveness meant, whether victim or perpetrator or even just by themselves, to put something that affects them rent free to put to rest, instead of occupying whatever unsolved crap that their body had to carry.
Whether it's a validation, a sign of acceptance from a wronged party (or themselves and their perceived wrong or lacking), or losing tension onto themselves in general, to no longer stay when it's overdue...
Some, just wanted to know if one is simply being remorseful and the assurance to do better or that to loosen the remorse from themselves...
It can vary, really.
Most of it was framed as something moralistic, or a sign of maturity.
But nah... I can very much also understand that it doesn't always meant it's healthy, possibly self serving in itself, or even question if the need itself to be "true".
But if I get rid of all that contextualize social and emotional crapity:
It boils down to a form of emotional or state transitioning, to end whatever was renting free in one's head and body, really, that itself leads into a closer to long term regulated state.