The full text of the Holy Father's remarks are up on the Vatican website (in Italian). He touches on a lot of things, and I'll share a few other snippets later, but on the issue of the role of women in the church, this is what he said (in John Allen's translation from this week's Word from Rome):
"I'll now respond to the assistant pastor of St. Jerome's - I can see he's also very young - who spoke to us about how much women do in the church, also on behalf of the priests. I can only underline how the special prayer for priests in the first Canon, the Roman Canon, always makes a great impression on me: Nobis quoque peccatoribus. In this realistic humility of us priests, precisely as sinners, we pray that the Lord will help us to be his servants. In this prayer for priests, and only in it, seven women appear who surround the priest. They demonstrate how women believers help us in our path. Everyone has certainly had this experience. In this way, the church owes an enormous debt of gratitude to women.I find that to be quite a powerful image: it's the Sacrament that governs, and through it, Christ himself. A huge reminder to all priests that they're not "in charge" per se, that it's not their own personal agenda. They're to be channels of Christ. I also love the refernce to the Canon of the Mass -- would that it were used more! (Even at the Sunday Mass at St. Peter's they used EPIII.)
You quite rightly underlined that, at the charismatic level, women do a great deal, and I would dare to say, a great deal for the governance of the church, beginning with the sisters of the great fathers of the church, such as St. Ambrose, to the great women of the Middle Ages - St. Hildegard, St. Catherine of Siena, then St. Teresa d'Avila - up to Mother Teresa. I would say that this charismatic sector certainly is distinct from the ministerial sector in the strict sense of the term, but it's a true and profound participation in the governance of the church. How could we imagine the governance of the church without this contribution, which sometimes becomes very visible, as when St. Hildegard criticized the bishops, or when St. Brigit and St. Catherine admonished the popes and obtained their return to Rome? It's always a determining factor, and the church can't live without it.
You rightly say: 'We want to see women more visibly, in a ministerial way, in the governance of the church.' I would say this is exactly the question. The priestly ministry from the Lord is, as we know, reserved to men. This priestly ministry is governance in the deep sense that, definitively, it is the Sacrament that governs the church. This is the decisive point. It is not the individual man who does something, but the priest faithful to his mission who governs, in the sense that it is the Sacrament - that is, through the Sacrament - that Christ himself governs, both through the Eucharist and the other sacraments, but it is always Christ who presides. However, it's proper to ask if in this ministerial service - the fact notwithstanding that here sacrament and charisma form the one track upon which the church is realized - it's not possible to offer more space, more positions of responsibility to women.
Now as to what this "more space" and "more positions of responsibility" would look like, is anyone's guess. But certainly, more women and lay people in general, in consultative and collaborative roles within the structure of the church. The lay ministry model that's developing in the US (not without it's problems -- most of which tend to be with an implicit and subtle clericalism, i.e., pretending that lay people are clerics and expecting them to behave as such) is one way.