2 The recourse we have to Mary in prayer follows upon the office she continuously fills by the side of the throne of God as Mediatrix of Divine grace; being by worthiness and by merit most acceptable to Him, and, therefore, surpassing in power all the angels and saints in Heaven. Now, this merciful office of hers, perhaps, appears in no other form of prayer so manifestly as it does in the Rosary. For in the Rosary all the part that Mary took as our co-Redemptress comes to us, as it were, set forth, and in such wise as though the facts were even then taking place; and this with much profit to our piety, whether in the contemplation of the succeeding sacred mysteries, or in the prayers which we speak and repeat with the lips. First come the Joyful Mysteries. The Eternal Son of God stoops to mankind, putting on its nature; but with the assent of Mary, who conceives Him by the Holy Ghost. Then St. John the Baptist, by a singular privilege, is sanctified in his mother's womb and favoured with special graces that he might prepare the way of the Lord; and this comes to pass by the greeting of Mary who had been inspired to visit her cousin. At last the expected of nations comes to light, Christ the Saviour. The Virgin bears Him. And when the Shepherds and the wise men, first-fruits of the Christian faith, come with longing to His cradle, they find there the young Child, with Mary, His Mother. Then, that He might before men offer Himself as a victim to His Heavenly Father, He desires to be taken to the Temple; and by the hands of Mary He is there presented to the Lord. It is Mary who, in the mysterious losing of her Son, seeks Him sorrowing, and finds Him again with joy. And the same truth is told again in the sorrowful mysteries.
Source: Iucunda Semper Expectatione (Vatican.va)