The rosary is a Christ-centered prayer. It brings us into meditation on the life of Christ.
The "Hail Mary" is a prayer which came from Gabriel, bringing the message from God himself, called her blessed among women.
We marvel at God's mercy and greatness, that He would be born of a woman to save us from our wretchedness.
We honor her as Christ did, and obey the last words she uttered in scripture, "Do whatever He tells you."