On the back of the Medal we see a large letter M with a cross above it. M is for Mary and Mother because she is indeed the Mother of God's people - a people founded on the twelve apostles, signified by the twelve stars arranged around the side. And God's people have learned to turn to their mother, knowing she will listen with a mother's sympathy and affection.
The two hearts are those of Jesus and Mary. God's message for Mary was one of suffering : "a sword will pierce your heart too" - just as the heart of her Son would be pierced by a soldier's lance. The showing of the two hearts is a reminder of God's love for us; Mother and Son united in the work of redemption as Christ offers himself on the Cross and Mary stands by that cross, assenting in faith so that the world might be saved.
The Medal, then, is a summary in itself of the Church's teaching on Our Lady - as well as a personal message to each one of us.