Always forgive your enemies; nothing annoys them so much. [Oscar Wilde]
The people criticized G-d and Moshe: "Why have you brought us up out of Egypt to die in the desert? There's no bread and no water, and we're sick of this unwholesome (manna) bread." G-d sent venomous snakes upon the people, and they bit the people. Many people of Israel died. The people came to Moshe and said "We have sinned! For we have spoken against G-d and against you! Pray to G-d that He should remove the snakes from us!" Moshe prayed on behalf of the people. [Chukas 21:5-7]
Even after the people criticized Moshe heavily, resulting in a punishment of venomous snakes, we nevertheless find that Moshe did not bear a grudge and prayed for the people to be saved. "From here we learn" writes Rashi, "that if a person asks you for forgiveness you should not be cruel and refrain from forgiving."
This principle is recorded by Rambam in his legal Code, the Mishneh Torah, in three places and there are a number of variations which need to be explained.
1) In Laws of Personal Injury, Rambam describes the method and process of forgiveness. "Once the attacker has asked forgiveness once, and then a second time, and we know that he has repented for his sin and he has abandoned the evil that he has done, then one must forgive him". However in Laws of Teshuvah these details are omitted. Instead, we are told that "When the sinner asks him for forgiveness, he should forgive him with a full heart and a willing spirit." Similarly, in Laws of Moral Conduct: "If the person returns and aks him for forgiveness, then he should forgive."
2) The person who forgives is given a different name in each of the three laws. In Laws of Moral Conduct he is called the "forgiver"; in Laws of Teshuvah a "person", and in Laws of Personal Injury he is called the "injured party".
3) One further detail is that in Laws of Teshuvah a person is told not to be "difficult to appease". Why does Rambam use this phrase, and why only in Laws of Teshuvah?
Forgiveness can be carried out on three levels:
1) When one person sins against another, he becomes liable to be punished for the sin that he committed. In order to be relieved of this punishment he needs to appease both G-d and the person that he sinned against. Therefore, through forgiving a person for his sin, one alleviates him from a Heavenly punishment.
2) A higher level of forgiveness is to forgive not just the act of sin but the sinner himself. i.e. even though one person may forgive another for a particular bad act (thus relieving him from being punished) there still may remain a trace of dislike for the person in general. Thus, a higher level of forgiveness is to forgive the entire person completely for his wrong, so that there remains no trace of bad feeling between them.
3) The highest level of forgiveness is an emotion that is so strong and positive that it actually uproots the sins of the past, making it as if they never occurred at all. After such a forgiveness, the sinner will be loved by the offended party to the very same degree that he was loved before the sin.
It is these three types of forgiveness which Rambam refers to in his three different laws:
1) In Laws of Personal Injury, Rambam discusses the laws of compensation for specific damages that one person causes another. Thus, when he speaks there of forgiveness for a sin, he is speaking of the forgiveness that is required to relieve the sinner from the punishment of that specific sin. Therefore, Rambam spells out the precise method of forgiveness that is required to achieve atonement ("when the attacker has asked forgiveness once, and then a second time, and we know that he has repented for his sin etc. then one must forgive him"), because only by following this precise method can we be sure that the sinner will be acquitted of this punishment.
To stress the point further, Rambam speaks in terms of an "injured party" and the "forgiving" of the injury, as we are speaking here of a specific sin and its atonement.
2) In Laws of Moral Conduct, the focus is not on the actual sin and its atonement, but rather, the character of the forgiver. And, if a person is to be of fine character, it is insufficient to forgive a person just so that he will be freed from punishment. Rather, one should forgive another person completely (i.e. the second level above). Therefore, in Laws of Moral Conduct, Rambam stresses that "When one person sins against another, he should not hide the matter and remain silent" for it would be a bad character trait to harbor resentment, keeping one's ill feelings to oneself. Therefore "it is a mitzvah for him to bring the matter into the open".
Thus, we can understand why Rambam omits here details of the process of forgiveness, for the main emphasis here is not the atonement of the sinner, but the required character traits of the victim.
To stress the point further, the person is termed here not as the "injured party" but as the "forgiver".
3) In Laws of Teshuvah, Rambam is speaking of the highest level of forgiveness which is required for a person to achieve a total "return to G-d". For this to occur, the forgiveness must be done in a manner that is so deep that one uproots the sin totally; as if it had never occurred at all. This is because total forgiveness is a crucial factor in the sinner's overall return to G-d, as Rambam writes: "Sins between man and his fellow man... are not forgiven until... the person has been asked for forgiveness..."
Thus, Rambam stresses here that "A person should be easily placated and difficult to anger, and when the sinner asks him for forgiveness, he should forgive him with a full heart and a willing spirit" (despite the fact that these details are more appropriate to Laws of Moral Conduct), because the goodwill of the victim is a crucial part of the sinner's teshuvah. Only when the victim is completely forgiving - to the extent that the sin is uprooted, as if it never existed - can we be sure that the sinner has returned to be as close to G-d as he was prior to the sin.
To stress this point further, Rambam writes "It is forbidden for a person (not an "injured party" or "forgiver") to be cruel and difficult to appease" - i.e. here we are not talking merely of the minimum forgiveness that is required to relieve the sinner from his punishment. Rather, here we are talking of the victim as a "person". And one can hope that he will not merely "forgive" his fellow who hurt him, freeing him from punishment, but that he will allow himself to be "appeased" completely, thereby helping his fellow Jew to come to a complete Teshuvah.
Source: Based on Likutei Sichos Vol 28 Lubavitcher Rebbe