From Fr. Paul of Graymoor:
Since the time that Christ Jesus walked this earth as the God-Man, there have been, over the centuries, numerous titles which have arisen to give honor to his most holy mother. In the early centuries of the Church, she was known as theotokos, or God-bearer, and as time passed, the Blessed Virgin Mary was honored with many other titles. Some of these titles are more widely known than others, but all convey a distinct attribute of Mary as a person who has found favor with God. Some of these titles describe her state of life, such as Our Lady of Grace. Others denote a location where she may have spoken spiritually to an individual, such as Our Lady of Fatima. In some titles of the Blessed Virgin Mary, she is associated with the redeeming work of her Son, and there are many such examples of this. But perhaps no other title in the world better describes the fullness of Mary's relationship with her Son as does the title of Our Lady of the Atonement.
The title embraces two mysteries of our faith: first, the atonement -- the wonderful at-one-ment which was achieved by our Lord Jesus Christ as He shed His Most Precious Blood upon the Cross at Calvary, through which came the reconciliation of man with God, and of man with man, making us "at one" in His Sacred Heart; and second, the role of Our Lady in the atonement wrought by God -- her coöperation with the Divine Will at the annunciation, and her participation in her Son's sufferings and death as she stood at the foot of the Cross. These words which Simeon spoke to her came to pass: "Behold, this child is destined for the fall and rise of many in Israel, and to be a sign that will be contradicted (and you yourself a sword will pierce) so that the thoughts of many hearts may be revealed." The crowning act of Redeeming Love -- the Atonement upon the Cross of Jesus Christ -- is for all of us the means whereby mankind finds salvation. Here Jesus gave us the greatest gift -- His precious life. Here he gave us His Blessed Mother. Here Mary stood -- here we stand, next to Her, at the foot of the Cross. We are children of The Atonement and the Blessed Virgin Mary, our Mother, is Our Lady who bears witness to Christ's Atonement.