A woman praying in solitude can do amazing things, but a woman praying as part of a deliberate army - much more.
Today I have been enrolled in St. Maximilian Kolbe's Militia Immaculata. I've just put myself on the front lines.
When I was contemplating becoming a Catholic, the single most difficult aspect was Marian theology. I'd heard that Catholics worshipped Mary, and although my head knew they did not, and understood the difference, a lot of behaviors by good Catholics sure felt like some kind of idolatry, and made me exceedingly uncomfortable.
It really makes a lot of sense, though, this business of Marian devotion. When Mary was greeted by the Angel, he addressed her by her title: "Full of Grace." It wasn't a courtesy - the angel was identifying Mary and her deepest, her innermost character. From her conception, she had been filled with God's grace in preparation of this immense privilege - of being the woman to give birth to the Messiah, to be the Ark of the New Covenant.
Jesus of Nazareth, the Second Person of the Holy Trinity, came to earth through a woman - and that woman's Fiat, her "Yes," is so integral and so far-reaching a part of God's plan of salvation that we lose a significant portion of it in ignoring it - and her.
He came to us through her, and to this day she is actively involved in bring us to Him. As the woman clothed with the sun (Rev. 12) is identified as Mary, whose firstborn is Jesus, we are her other children - hers by adoption, according to the language of St. Paul. She is our mother, and she assists in our spiritual re-birth, in our discipleship and our total journey toward Heaven. She intercedes for us even as she interceded on behalf of the poor couple in Cana, who had run out of wine at their wedding feast.
Her few recorded words serve as instruction ("Do whatever he tells you!") and example ("Be it done to me according to thy word") - and as inspiration (the great hymn of praise, the Magnificat, in Luke 1)
King Solomon, a type of Christ, placed his mother on a throne (I Kings 2:19). Mary sits on a throne, also, crowned with the glory her Son gives to her - and there she intercedes for us all.
As the woman clothed with the sun, Mary is not some frightened potential victim of the Devil - she is obedient to God in all things - and being the bearer of the one who will crush the head of the serpent, she is intimately engaged in the great battle which rages around us now. She - and her Son - will be victorious in the end, but there is no better example we can have of obedience to God, or help in attaining that obedience - or of fidelity or strength. She was with her Son from the time of the Angel's Visitation (see that painting in my heading, again) - until and through the birth of the Church. The only significant event she is not recorded being present for? - the Last Supper, when her Son instituted the Holy Eucharist and the Holy Priesthood.
If she is the handmaid of the Lord, then in being her handmaid, we do well in serving Him.