Pointed out by one of the greatest Marian saints of all times, St. Louis de Montfort.
Here is his explanation:
After you have invoked the Holy Spirit, in order to say your Rosary well, place yourself for a moment in the presence of God and make the offering of the decades …
Before beginning a decade, pause for a moment or two, depending on how much time you have, and contemplate the mystery that you are about to honor in that decade. Always be sure to ask, by this mystery and through the intercession of the Blessed Virgin, for one of the virtues that shines forth most in this mystery or one of which you are in particular need.
Take great care to avoid the two pitfalls that most people fall into during the Rosary:
The first is the danger of not asking for any graces at all, so that if some good people were asked their Rosary intention they would not know what to say. So, whenever you say your Rosary, be sure to ask for some special grace or virtue, or strength to overcome some sin.
The second fault commonly committed in saying the Rosary is to have no intention other than that of getting it over with as quickly as possible. This is because so many look upon the Rosary as a burden, which weighs heavily upon them when it has not been said, especially when we have promised to say it regularly or have been told to say it as a penance more or less against our will.