Mary's perpetual virginity is an article of our faith. We Catholics believe that our Blessed Mother was a virgin before and after the birth of Jesus. (The “brothers and sisters” of Jesus we hear about in the Gospels are, actually, his cousins or perhaps half-siblings.) Mary was given to no man so that she could be given to each of us. That is the significance of Mary's virginity.
Another reason Mary's virginity is significant is because of its effect on marriage. Mary was truly married to Joseph, yet she remained a virgin. Mary thus adds a "virginal" component to marriage. She is a model for married couples. Husbands and wives obviously give themselves to each other intimately and physically in marriage, but they also should have a sense of virginity about them.
Virginity means openness or newness. If an adult going to Great America, for example, can act like it's his first time, the rides will be thrilling and the experience more rewarding.
This is because God creates out of nothing. “In the beginning, when God created the heavens and the earth, the earth was a formless wasteland, and darkness covered the abyss, while a mighty wind swept over the waters” (Gen 1:1). Just as the wind or the spirit swept over the barrenness, the Holy Spirit overshadowed the barren womb of Mary (cf. Lk 1:35). Infertility, through God's grace, is fruitful. It's through a person's virginity that God can create and recreate. If spouses can maintain a spiritual virginity in their marriage, God will continue to make their marriage fruitful. This is a dynamic of marriage that would not otherwise be present if Mary had not been a virgin. That is why we call her the Virgin Most Fruitful.