The rosary is a very important prayer, even more so today when faith is threatened by so many things in our secular culture: a growing atheism, secularism, and humanism that seeks to order human society without God.
Genesis 3:15, a text called the Proto-evangelium because it is the first announcement of the Good News, has often been read in the Church in the light of Mary's role. The woman spoken of there will crush the head of Satan:
"I will put enmity between you and the woman,
and between your offspring and hers;
he will strike your head,
and you will strike his heel."
Think about that. God himself has put enmity between Satan and Mary. So Mary has a particular power in crushing the forces of evil. That's why the rosary is a powerful prayer. When we pray it, we are stepping into that divinely established way that God wants to protect his children and defeat Satan.
On the feast of the Assumption last August, Pope Francis spoke about this too:
"Mary accompanies us, struggles with us, sustains Christians in their fight against the forces of evil. Prayer with Mary, especially the rosary – but listen carefully: the Rosary. Do you pray the Rosary every day? But I’m not sure you do [the people shout “Yes!”]… Really? Well, prayer with Mary, especially the Rosary, has this “suffering” dimension, that is of struggle, a sustaining prayer in the battle against the evil one and his accomplices. The Rosary also sustains us in the battle."