The prayer asks Mary to "Reign over individuals and over families, as well as over societies and nations."
In the Catholic Church, it is believed that Mary is the "Queen Mother," following an ancient Jewish tradition that the mother of the king is known as the "queen."
Since Jesus is recognized as the King of kings, the Virgin Mary is in turn the Queen, who can plead our case before her Son.
Here is a prayer composed by Pope Pius XII to Mary, Queen of Heaven.