Our Lady has asked us repeatedly to pray the rosary for world peace (see aparations...especially Fatima). The rosary is a spiritual weapon against the evil one. Our Lady has made promises to those who faithfully pray the rosary.
Why Mary?

By honoring the Mother of God we honor God himself, her creator and redeemer. By imitating Mary we become better disciples of Jesus: we follow him, we hold his words and deeds in our very hearts, and ponder what we do not fully understand as she did. We say humbly to God, "Behold the servant of the Lord…Let it be according to your will." And we follow him. And we stand tall in times of darkness and keep believing when it is hard to do so. We give what is near and dear to us to the world –even knowing that it will end in death and destruction, and hope in the Lord that it will somehow work out in the end. We forgive. We mother. We witness. We pray. ~All these things are in the rosary!