1.Whosoever shall faithfully serve me by the recitation of the Rosary shall receive signal graces
Signal Graces are those special and unique Graces to help sanctify us in our state in life. See the remaining promises for an explanation for which these will consist. St. Louis de Montfort states emphatically that the best and fastest way to union with Our Lord is via Our Lady
2.I promise my special protection and the greatest graces to all those who shall recite the Rosary
Our Lady is our Advocate and the channel of all God's Grace to us. Our Lady is simply highlighting that She will watch especially over us who pray the Rosary.
3.The Rosary shall be a powerful armor against hell, it will destroy vice, decrease sin and defeat heresies.
This promise, along with the next, is simply the reminder on how fervent prayer will help us all grow in holiness by avoiding sin, especially a prayer with the excellence of the Rosary. An increase in holiness necessarily requires a reduction in sin, vice, and doctrinal errors (heresies). If only the Modernists could be convinced to pray the Rosary! St. Louis de Montfort states "Since Mary alone crushed all heresies, as we are told by the Church under the guidance of the Holy Spirit (Office of the Blessed Virgin Mary)..."
4.It will cause good works to flourish; it will obtain for souls the abundant mercy of God; it will withdraw the hearts of men from the love of the world and its vanities, and will lift them to the desire for Eternal Things. Oh, that souls would sanctify themselves by this means.
This promise, along with the previous, is the positive part, that being to live in virtue. Becoming holy is not only avoiding sin, but also growing in virtue
5.The soul which recommends itself to me by the recitation of the Rosary shall not perish.Since Our Lady is our Mother and Advocate, She always assists those who call on Her implicitly by praying the Rosary
The Church reminds us of this in the Memorare prayer, "... never was it known that anyone who fled to your protection, implored your help or sought your intercession, was left unaided ..."
6.Whosoever shall recite the Rosary devoutly, applying himself to the consideration of its Sacred Mysteries shall never be conquered by misfortune. God will not chastise him in His justice, he shall not perish by an unprovided death; if he be just he shall remain in the grace of God, and become worthy of Eternal Life.
This promise highlights the magnitude of Graces that the Rosary brings to whomever prays it. One will draw down God's Mercy rather than His Justice and will have a final chance to repent (see promise #7). One will not be conquered by misfortune means that Our Lady will obtain for the person sufficient Graces to handle said misfortune (i.e. carry the Crosses allowed by God) without falling into despair. As Sacred Scripture tells us, "For my yoke is sweet and my burden light."
7.Whoever shall have a true devotion for the Rosary shall not die without the Sacraments of the Church.
This promise highlights the benefits of obtaining the most possible Graces at the hour of death via the Sacraments of Confession, Eucharist, and Extreme Unction (Anointing of the Sick). Being properly disposed while receiving these Sacraments near death ensures one's salvation (although perhaps with a detour through Purgatory) since a final repentance is possible.
8.Those who are faithful to recite the Rosary shall have during their life and at their death the Light of God and the plenitude of His Graces; at the moment of death they shall participate in the Merits of the Saints in Paradise.
Our Lady highlights the great quantity of Graces obtain through praying the Rosary, which assist us during life and at the moment of death. The merits of the Saints are the gift of God's rewards to those persons who responded to His Grace that they obtained during life, and so Our Lady indicates that She will provide a share of that to us at death. With this promise and #7 above, Our Lady is providing the means for the person to have a very holy death.
9.I shall deliver from purgatory those who have been devoted to the Rosary.
Should one require Purgatorial cleansing after death, Our Lady will make a special effort to obtain our release from Purgatory through Her intercession as Advocate.
10.The faithful children of the Rosary shall merit a high degree of Glory in Heaven.
This promise is a logical consequence of promises #3 and #4 since anyone who truly lives a holier life on earth will obtain a higher place in Heaven. The closer one is to God while living on earth, the close that person is to Him also in Heaven. The Catechism of the Catholic Church states "Spiritual progress tends toward ever more union with Christ."
11.You shall obtain all you ask of me by recitation of the Rosary
This promise emphasizes Our Lady's role as our Advocate and Mediatrix of all Graces. Of course, all requests are subject to God's Most Perfect Will. God will always grant our request if it is beneficial for our soul, and Our Lady will only intercede for us when our request is good for our salvation.
12.All those who propagate the Holy Rosary shall be aided by me in their necessities
If one promotes the praying of the Rosary, Our Lady emphasizes Her Maternal care for us by obtaining many Graces (i.e. spiritual necessities) and also material necessities (neither excess nor luxury), all subject to the Will of God of course.
13.I have obtained from my Divine Son that all the advocates of the Rosary shall have for intercessors the entire Celestial Court during their life and at the hour of death
Since Our Lady is our Advocate, She brings us additional assistance during our life and at our death from all the saints in Heaven (the Communion of Saints)
14.All who recite the Rosary are my Sons, and brothers of my Only Son Jesus Christ
Since the Rosary is a most excellent prayer focused on Jesus and His Life and activities in salvation history, it brings us closer to Our Lord and Our Lady. Doctrinally, Our Lady is our Mother and Jesus is our Eldest Brother, besides being our God.
15.Devotion to my Rosary is a great sign of predestination
Predestination in this context means that, by the sign which is present to a person from the action of devoutly praying the Rosary, God has pre-ordained your salvation. Absolute certainty of salvation can only be truly known if God reveals it to a person because, although we are given sufficient Grace during life, our salvation depends upon our response to said Grace. (See Summa Theologica, Question 23 for a detailed theological explanation). Said another way, if God has guaranteed a person's salvation but has not revealed it to Him, God would want that person to pray the Rosary because of all the benefits and Graces obtained. Therefore the person gets a hint by devotion to the Rosary. This is not to say that praying the Rosary guarantees salvation - by no means. In looking at promises #3 and #4 above, praying the Rosary helps one to live a holy life, which is itself a great sign that a soul is on the road to salvation. In fact, St. Louis de Montfort says even more strongly that "an infallible and unmistakable sign by which we can distinguish a heretic, a man of false doctrine, an enemy of God, from one of God's true friends is that the hardened sinner and heretic show nothing but contempt and indifference to Our Lady..."