First, what is it? Forgiveness is releasing your enemy from a certain debt owed to you, immoderate anger and bitterness, and temptation to immoderate anger and bitterness. It means wishing peace and well-being on your enemy, and ultimately eternal life for them. The purpose is maintaining peace on Earth between people, including towards our enemies.
It prevents unnecessary conflict and discord. But even more, it is a remedy for the pride that rises up in us due to original sin as a result of injustice. It heals us of trauma and harm done to us on lower levels, and it keeps the soul healthy and balanced even in the center of extreme persecution. Ultimately, it is for preserving or gaining holiness in the face of persecution. It benefits the most the victim.
Second, what is it not? It does not always mean releasing legal debts collected through law and legal authority, or to avoid legal punishment. Sometimes the enemy causes a level of harm that requires properly submitted formal grievances to proper authority, for the sake of punishment and restitution. And that authority and process under the law does not always directly involve secular or church government, while it does indirectly and potentially, but natural authorities and social processes sanctioned by law.
There is in contrast a debt we cannot collect, which we must forgive or release the enemy from, otherwise it would mean seeking revenge, but God Himself, rest assured, collects that debt, not us. Forgiveness also does not mean forgetting the essential injustices of the past to prevent them from happening again, and to others. It does not mean reconciliation unless the enemy is repentant, and even then prudence dictates if there should be reconciliation, which is more obligatory between spouses or other family members, but even then severe circumstances can dictate keeping a permanent distance.
Forgiveness can be distinguished between an act towards the repentant vs. the unrepentant. You must always forgive everyone, but not in the sense of reconciliation unless the enemy apologizes and makes amends. God does not forgive the unrepentant sinner of their sin, just as the priest is taught to withhold absolution if the penitent appears without remorse.
When someone is guilty of mortal sin, they break the relationship with God, and God then withdraws friendship until they repent. We imitate this by not pretending to be friends with false friends who are enemies in disguise. But true forgiveness is a choice to be disposed to immediately accept an apology once sincerely given, even from the worst of enemies. It is a choice to be ready for that if it ever happens, even though in this heartless, unrepentant, proud age, true repentance and reconciliation is not commonplace, whether it is a person reconciling to God, or to the person they injured.
It is moral relativism that has blurred the moral precepts and malformed consciences to be blind to sin. Not only the more easy to identify sins of the flesh, such as fornication or drunkenness, but sins of the spirit, in pride, rash judgment, slander, detraction, calumny, envy, or wrath. Pride itself can make a person blind or indifferent to the fact they commit those sins. So the task of forgiveness, and ideally reconciliation on some level, can be very complex.
Forgiveness is both spiritual and psychological. The former needs to be immediate or quick, to avoid falling into the sin of unforgiveness which can damn the soul if grave. But the latter takes time, often years when the injustices were serious, over years, between family members or close friends, that is the closer the relationship. It takes a process of healing, the main purpose to heal the mind from past trauma caused by the enemy. And if psychological forgiveness takes time, that is not sinful.
This takes practice I am learning to make a better habit. The goal is "holy forgetfulness" in which you learn over time to forget the traumatic emotions and nitty gritty details of past traumatic events. Over time those disappear from the unconcious, subconscious, and conscious mind. At most what is left are the bare basic facts of the past for self-protection. Daily meditation to achieve this is the remedy.
I hope this helps. It comes from traditional Catholic sources. And these are details I have achieved clarity about only recently, at least more clarity. And that is as much as I can say about that because, as I said, forgiveness is a paradox. A holy, positive paradox, but nonetheless a paradox. Yet still, we are called to endlessly forgive until we die, as a requirement for salvation.