The Sunday of Forgiveness, the last of the preparatory Sundays before Great Lent, has two themes: it commemorates Adam’s expulsion from Paradise, and it accentuates our need for forgiveness. There are obvious reasons why these two things should be brought to our attention as we stand on the threshold of Great Lent. One of the primary images in the 
Triodion is that of the return to Paradise. Lent is a time when we weep with Adam and Eve before the closed gate of Eden, repenting with them for the sins that have deprived us of our free communion with God. But Lent is also a time when we are preparing to celebrate the saving event of Christ’s death and rising, which has reopened Paradise to us once more (Luke 23:43). So sorrow for our exile in sin is tempered by hope of our re-entry into Paradise.
The second theme, that of forgiveness, is emphasized in the Gospel reading for this Sunday (Matthew 6:14-21) and in the special ceremony of mutual forgiveness at the end of the Vespers on Sunday evening. Before we enter the Lenten fast, we are reminded that there can be no true fast, no genuine repentance, no reconciliation with God, unless we are at the same time reconciled with one another. A fast without mutual love is the fast of demons. We do not travel the road of Lent as isolated individuals but as members of a family. Our asceticism and fasting should not separate us from others, but should link us to them with ever-stronger bonds.
The Sunday of Forgiveness also directs us to see that Great Lent is a journey of liberation from our enslavement to sin. The Gospel lesson sets the conditions for this liberation. The first one is fasting—the refusal to accept the desires and urges of our fallen nature as normal, the effort to free ourselves from the dictatorship of the flesh and matter over the spirit. To be effective, however, our fast must not be hypocritical, a “showing off.” We must “appear not unto men to fast but to our Father who is in secret” (vv. 16-18). The second condition is forgiveness—”If you forgive men their trespasses, your Heavenly Father will also forgive you” (vv. 14-15). The triumph of sin, the main sign of its rule over the world, is division, opposition, separation, hatred. Therefore, the first break through this fortress of sin is forgiveness—the return to unity, solidarity, love. To forgive is to put between me and my “enemy” the radiant forgiveness of God Himself. To forgive is to reject the hopeless “dead ends” of human relations and to refer them to Christ. Forgiveness is truly a “breakthrough” of the Kingdom into this sinful and fallen world.
from John Sanidopoulos, “Sunday of Forgiveness: Cheesefare Sunday”, 2010. Complete text here.
The Rite of Forgiveness typically occurs immediately after the Liturgy concludes on the Sunday of Forgiveness. During the rite, all the faithful approach the priest and one another, asking for mutual forgiveness. Fr. Alexander Schmemann comments:
One may ask, however: Why should I perform this rite when I have no “enemies”? Why should I ask forgiveness from people who have done nothing to me, and whom I hardly know? To ask these questions, is to misunderstand the Orthodox teaching concerning forgiveness. It is true, that open enmity, personal hatred, real animosity may be absent from our life, though if we experience them, it may be easier for us to repent, for these feelings openly contradict Divine commandments. But, the Church reveals to us that there are much subtler ways of offending Divine Love. These are indifference, selfishness, lack of interest in other people, of any real concern for them — in short, that wall which we usually erect around ourselves, thinking that by being “polite” and “friendly” we fulfill God’s commandments. The rite of forgiveness is so important precisely because it makes us realize—be it only for one minute—that our entire relationship to other men is wrong, makes us experience that encounter of one child of God with another, of one person created by God with another, makes us feel that mutual “recognition” which is so terribly lacking in our cold and dehumanized world.