To forgive is to grant pardon without harboring resentment:
glowing cross
 The Christian has tasted the free gift that comes from heaven. It is only in Christ that a man can be at peace with God. Forgiveness is not something he can ever win; it is a free gift. It is only when he comes to the Cross that his burden is rolled away. The Christian is a man who knows the immeasurable relief of experiencing the free gift of the forgiveness of God.

15.  And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance.
 16.  For where a testament is, there must also of necessity be the death of the testator.[
A man who makes and leaves a will, or testament, at death.]

 17.  For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth.
 18.  Whereupon neither the first testament was dedicated without blood.
 19.  For when Moses had spoken every precept to all the people according to the law, he took the blood of calves and of goats, with water, and scarlet wool, and hyssop, and sprinkled both the book, and all the people,
 20.  Saying, This is the blood of the testament which God hath enjoined unto you.
 21.  Moreover he sprinkled with blood both the tabernacle, and all the vessels of the ministry.
 22.  And almost all things are by the law purged with blood; and without shedding of blood is no remissi

Jesus Reserected
Forgiveness is a costly thing. Human forgiveness is costly. A son or a daughter may go wrong and a father or a mother may forgive; but that forgiveness brings tears, whiteness to the hair, lines to the face, a cutting anguish and then a long dull ache to the heart. It does not cost anything. Divine forgiveness is costly. God is love but he is also Holiness. He least of all can break the great moral laws on which the universe is built. Sin must have its punishment or the very structure of life disintegrates. And God alone can pay the terrible price that is necessary before men can be forgiven. Forgiveness is never a case of saying: "It's all right; it doesn't matter." It is the most costly thing in the world. Without the shedding of heart's blood there can be no forgiveness of sins.
Nothing brings a man to his senses with such arresting violence as to see the effect of his sin on someone who loves him in this world or on the God who loves him forever, and to say to himself: "It cost that, to forgive my sin." Where there is forgiveness someone must be crucified.
Jesus on the cross

 John uses the curious phrase through his name (1Jn.2:12). Forgiveness comes through the name of Jesus Christ. The Jews used the name in a very special way. The name is not simply that by which a person is called; it stands for the whole character of a person in so far as it has been made known to men. This use is very common in the Book of Psalms. "Those who know thy name put their trust in thee" (Ps.9:10). This clearly does not mean that those who know that God is called Yahweh (HSN3068 and HSN3069) will put their trust in him; it means that those who know God's nature in so far as it has been revealed to men will be ready to put their trust in him, because they know what he is like. The Psalmist prays: "For thy name's sake, O Lord, pardon my guilt" (Ps.25:11), which to all intents and purposes means for thy love and mercy's sake. The grounds of the Psalmist's prayer are the character of God as he knows it to be. "For thy name's sake," prays the Psalmist, "lead me, and guide me" (Ps.31:3).
He can bring his request only because he knows the the name--the character of God. "Some boast of chariots," says the Psalmist, "and some of horses; but we boast of the name of the Lord our God" (Ps.20:7). Some people put their trust in earthly helps but we will trust God because we know his nature.

Matthew 6:14-15
 14.  For if ye forgive men their trespasses, your heavenly Father will also forgive you:
 15.  But if ye forgive not men their trespasses, neither will your Father forgive your trespasses.
Matthew 18: 21.  Then came Peter to him, and said, Lord, how often shall my brother sin against me, and I forgive him? till seven times?
 22.  Jesus saith unto him, I say not unto thee, Until seven times: but, Until seventy times seven.

[also read: Matthew 18:23-35]

Mark 11;25-26
25.  And when ye stand praying, forgive, if ye have ought against any: that your Father also which is in heaven may forgive you your trespasses.
 26.  But if ye do not forgive, neither will your Father which is in heaven forgive your trespasses.

There is one sin that is not forgiven :
28.  Verily I say unto you, All sins shall be forgiven unto the sons of men, and blasphemies wherewith soever they shall blaspheme:
 29.  But he that shall blaspheme against the Holy Ghost hath never forgiveness, but is in danger of eternal damnation:

further study~> The Golden rule