The Power of Intercessory Prayer:
The saints of the Old Law and the New Law, the 12 Patriarchs and the 12 Apostles, intercede for those on earth.
James 5:16b "the fervent prayer of a righteous man is very powerful."
Rev. 5:8 "When he took it, the four living creatures and the twenty-four elders fell down before the Lamb. Each of the elders held a harp and gold bowls filled with incense, which are the prayers of the holy ones.
Rev. 8:3 “Another angel came and stood at the altar, holding a gold censer. He was given a great quantity of incense to offer, along with the prayers of all the holy ones, on the gold altar that was before the throne.”
Vain repetition is mindless babbling not repeated prayer
The purpose of the different beads on the rosary is to count the various prayers as they are said. Unlike the Moslem prayer beads and the mantras of Buddhism, the prayers of the rosary are meant to occupy our whole being, body and soul, in meditating on the truths of the Faith. Simply to repeat prayers is not the vain repetition condemned by Christ (Mt 6:7), since He Himself repeats His prayer in the Garden three times (Mt 26:39, 42, 44) and the Psalms (inspired by the Holy Spirit) are often very repetitive (Ps 119 has 176 verses and Ps. 136 repeats the same phrase **26 times**).
Matthew 6:7 In praying, do not babble like the pagans, who think that they will be heard because of their many words.
Praise the LORD, who is so good;
God’s love endures forever;
 Praise the God of gods;
God’s love endures forever;
. . .
 Praise the God of heaven,
God’s love endures forever.
Matthew 26:39 He advanced a little and fell prostrate in prayer, saying, “My Father, if it is possible, let this cup pass from me; yet, not as I will, but as you will.”
Matthew 26:42 Withdrawing a second time, he prayed again, “My Father, if it is not possible that this cup pass without my drinking it, your will be done!”
Matthew 26:44 He left them and withdrew again and prayed a third time, saying the same thing again.
The Church believes that it is necessary for a Christian to meditate (prayerfully think about) the will of God, the life and teachings of Jesus, the price He paid for our salvation, and so on. Unless we do this we will begin to take these great gifts for granted and ultimately fall away from the Lord. Every Christian must meditate in some way in order to preserve the gift of salvation (James 1:22-25). Many Catholic and non-Catholic Christians prayerfully read and apply Scripture to their lives - that too is meditation.
The rosary is an aid to meditation. As one prays the rosary, the hands, the lips, and to a certain extent the mind, are occupied with the Creed, the Our Father, the Hail Mary and the Glory Be. At the same time one is supposed to meditate on one of 15 mysteries, from the Annunciation through the Passion, to the Glorification. By means of the rosary we learn what makes true holiness (“let it be done to me according to thy word”), about the great gift of salvation (“It is finished!”) and the great rewards God has in store for us (“He is Risen”). Even Mary’s own rewards (Assumption and Glorification) anticipate and teach us about our own sharing in the reign of Christ.
The faithful recitation of the rosary according to this pattern has been found by Catholics to be the door to greater gifts of prayer and holiness, as shown by the many canonized saints who have practiced and recommended the rosary, as does the Church.
Answered by Colin B. Donovan, STL