What is the origin and meaning of the rosary? What is the origin and meaning of the rosary?
It’s a repetitive customary prayer of “Hail Mary, the lord’s prayer, glory be, and oh my Jesus”.
Short answer, another name for the Rosary is the Angelic Psalter.  It is a repetition mainly of the words of the Angel Gabriel to the Blessed Virgin Mary announcing the Birth of Jesus and the words spoken by St. Elizabeth when Mary visited her shortly before the birth of John the Baptist, when he &quot;leapt in her womb&quot;.  The reason for its simplicity is that it is for lay-people to pray who wouldn't have access to a regular psalter, like priests and other religious would have.  Originally, there were 150 Hail Marys which was close enough to the 150 Psalms in the Book of Psalms.

From the time Saint Dominic established the devotion to the holy Rosary up to the time when Blessed Alan de la Roche re-established it in 1460, it has always been called the Psalter of Jesus and Mary. This is because it has the same number of Hail Marys as there are psalms in the Book of the Psalms of David. Since simple and uneducated people are not able to say the Psalms of David, the Rosary is held to be just as fruitful for them as David's Psalter is for others.
St. Louis De Montfort - The Secret of the Rosary

While praying the Rosary, for repetitions of the Hail Mary, you're expected to meditate on one of the central events or themes of the Gospel and/or the Life of Mary.  Like I said, originally there were 15 decades with 3 groups of mysteries (Joyful: pertaining to the Birth of Jesus; Sorrowful: Pertaining to His Passion; Glorious: Pertaining to events after the Resurrection) or thing to mediate on, in 2000, the Year of the Rosary, St. John Paul II added another Mystery (the Luminous Mysteries, which are about the works of Jesus).  People who pray the Rosary every day rotate between these mysteries with one to think about every day, almost like priests will do with the Liturgy of the Hours.
The origin of the Rosary itself are a little nebulous as it seems to have been given and redicovered several times since the turn of the second millennium (St. Domininc and Alan De La Roche being key figures).  But from all the Visions and Marian Apparitions (Fatima especially) it's clear that Our Lady wants us praying the Rosary.
The reason there are 10 Hail Mary's in each decade is interesting, especially since I never considered it before figured it just came naturally like a clock with 12 numbers on it. But there is special significance to the number 10

The Dominican tradition consolidated the combination of Hail Marys and events of Jesus' life added to each Hail Mary. Over time fifteen mysteries (events of Jesus' life) were retained and combined with the Hail Marys for each one of the mysteries. Independently from this historical reason, there is a symbolic reason. Ten has the meaning of totality and unity, meaning that each one of Christ's mysteries is part of his total person and work and expresses its unity and totality, as well as its thorough contemplation by the person who says this decade of the rosary.
Why 10 Hail Mary's

The most widely read history of the Rosary can be found in St. Louis De Montfort's Secret of the Rosary a much better answer than mine can be found in Pope John Paul II's encyclical Rosarium Viginis Mariae

The Rosary of the Virgin Mary, which gradually took form in the second millennium under the guidance of the Spirit of God, is a prayer loved by countless Saints and encouraged by the Magisterium. Simple yet profound, it still remains, at the dawn of this third millennium, a prayer of great significance, destined to bring forth a harvest of holiness. It blends easily into the spiritual journey of the Christian life, which, after two thousand years, has lost none of the freshness of its beginnings and feels drawn by the Spirit of God to “set out into the deep” (duc in altum!) in order once more to proclaim, and even cry out, before the world that Jesus Christ is Lord and Saviour, “the way, and the truth and the life” (Jn 14:6), “the goal of human history and the point on which the desires of history and civilization turn”.