How is forgiveness defined in Buddhism?

Forgiveness explained in budhdism is tolerance. If someone does a harm on you it is non of your bussiness. That person will bring the karma for what he did. If you avenge it is something you are collecting. So tolerance is the best option.

Householder, interested,

the question seems to mix up two aspects, one of the actor having done harm, and one of the receiver of harm from another.

As for the actor who had done harm it's important to recognize such and ask for forgiveness from the victim of his deed if such is possible. Even if not, what might be often the case, one should confess a wrong doing by speech or bodily deeds toward a good friend on the path (teacher, preceptor) and resolve to not doing again. Depended on the case and relation one also accepts a certain punishment for good rehabilitation if in an community. When this is done, one counts as clean again and has been "lift up from the transgression". Of course such would not make the deed undone and effect will nevertheless fall back on one, but one is able to progress one way upward and on the path. Such is not possible if not seeing a fault or not willing to confess it.

As for forgiveness, being one who was touched by a faulty deed, one aspect is to bear much as possible, which is called "metta" and "khanti" and look that no ill-will on such is nourished. Further, the second fool next one not seeing and confessing ones own faults is a person who does not except (even) a pardon. Such bearing of ill-will is a fault as well and also hinders one to progress.

If one holds wrong views and thinks in manners of rights, one will be always either the first or the second foolish person.

It's a huge and important topic, focusing not only on harmony but also on the prerequisite for the practice: Right view.

Some further aspects and sources are mentioned here.

See also:

• Reconciliation, Right & Wrong, by Ven. Thanissaro Bhikkhu
• Wisdom over Justice
• Justice vs. Skillfulness
• Verdrängen ist nicht Verzeihen (German language)

(Note that this is not given for trade, exchange, stacks, entertainment and akusala deeds, but as a share of merits and continue such for release)

I am not deeply learned in Buddhist doctrine, but there are a couple ideas I discovered that I think add insight to the other responses to your question. The first idea is that human life is essentially suffering. I believe this is called the first of the four noble truths. It follows from it that you can, as a human being, feel compassion for any other human being. The possibility of forgiveness is inherent in this idea.

The other idea is that all phenomenon arise from causes and conditions. Violence is not exercised in a vacuum, but is a result of other events and conditions experienced by the perpetrator in combination with the perpetrator's not having risen above them. These events and conditions include, aside from the easily understood concept of 'violence begets violence', what my source termed "afflictive emotions", a concept akin to the idea that we are all programmed to an extent by our biology and so naturally feel emotions such as lust, anger, jealousy that might lead one to harming another person. Adopting this perspective of causes and conditions, I find, tends to dissolve the hatred and enmity I have felt towards people who caused me harm.

You said, "Forgiveness means if anybody do some harm to you you don't react and just try to pretend like it never happened to you."

This is called "Kshanti-paramita", the perfection of patience.

In Buddhism, patience does not mean that you put a lot of effort to keep yourself calm. In Buddhism, patience means you do not have attachments. Because you have no attachments, you can not be offended.

The biggest attachment is Ego, the feeling of self-significance in the world. When you feel you are significant, and people do something that shows that you are not, you can easily feel insulted and lose temper. So Ego is like a big sore, very sensitive, that makes you very vulnerable.

Other types of attachments are attachment to religion, attachment to "we", attachment to some sort of theory, attachment to intellect, attachment to purity etc.

When you have no attachments, no Ego, no self-significance - you become very patient. You become unmovable, invulnerable. This is called perfection of patience.