Repeating the same prayer over and over again is a help for meditation, calming and focusing our minds and bodies, and allowing the words to sink into us through repetition.
Jesus has given great authority to Mary to work in the world. For example, at Fatima in 1917, Mary told the three visionaries Lucia, Francisco, and Jacinta, “Pray the Rosary every day in honor of Our Lady of the Rosary to obtain peace in the world . . . for she alone can save it.”
The different mysteries are opportunities to meditate on different parts of Jesus’ life, death, and resurrection.
The rosary is a way to honor Mary, just as Jesus honored his own Mother.