The Lord God set down a Day of Atonement for the Hebrews, while they wandered in the desert.  This day was fulfilled by The Lord Jesus when he died for our sins.  The Day of Atonement under the New Law, then, is the day we call Good Friday.    In his work, "On the Divine Duties", the scholar and master teacher Alcuin (d. 804), describes the nature of the various holy days of the Church.  In the following excerpt, he discusses Good Friday, and the meaning of Christ's suffering for us:

"  'Parasceve' is interpreted as 'The Preparation', which is the sixth day of the week, the day before the Sabbath.  On this day, the Jews prepared those things which were necessary for the Sabbath, in accord with what was ordered in regards to the manna: 'On the sixth day, you shall gather a double portion' (Exodus 16, 5).  And this is understood of this solemnity [of Good Friday], for Christ explained the mystery of the Cross on that day: that he came into this world so that we who were punished in Adam by a tree, might be healed through the mystery of another Tree.  The gentle power of Christ shows the reason of this triumph, celebrated through the whole world every year, for he deigned to redeem the sins of the world by the Blood of his Passion, and to absolve our sins by his Death on the Cross.  

"The three-fold reason for The Lord's Passion is shown on this day.  First, that the redemption of Christ might be given for the guilt of the world, and that the ancient enemy be hooked by the cross-beam of the Cross -- so that the devil would vomit forth those whom he had devoured, not forced by physical power, but by justice.  Second, to show the men following him [The Lord] the teaching on life: for this, he ascended a Cross and gave an example of his Death and Resurrection to us.  The third reason he hung on the Cross was to humble the pride of the world and its puffed-up wisdom through the 'foolishness' of the Cross, as it is accounted, making clear that the 'foolishness' of God is so much wiser than men."