The holy days immediately after Christmas are a curious mix. We start with St. Stephen the Proto-Martyr, the first specifically and explicitly Christian martyr, and whose martyrdom is a sort of template for other martyrdoms. We then move to St. John the Evangelist, who is according to tradition the only apostle who wasn't martyred (he was exiled, not killed). And today we meet the Holy Innocents, who are the martyrs least like anything we expect martyrs to be.
The mix did not escape our predecessors. Aquinas mentions somewhere a sermon by St. Bernard of Clairvaux arguing that there were three kinds of martyrdom: martyrdom in will but not in physical death, as with St. John; martyrdom in will and in physical death, as with St. Stephen; and martyrdom in physical death but not in will, as with the Holy Innocents.
Genuine martyrdom is an act of witness; but to be the sort of martyrdom celebrated by the Church it must be an act of God. As typically understood, this is by the way of the infused virtue of fortitude, which is to say, inspired fortitude, whose most encompassing act is witness in violent death. In St. Stephen we see this full complete sense of martyrdom: God acts as principal agent of the witness, Stephen through inspired fortitude is the instrumental agent of witness, and the act is able, in context, to be a complete act of witness in violent death. The relation of this to St. John is easy to see: God still acts as principal agent of John's witness, John through inspired fortitude is still instrumental agent of the witness, but as it happens the fortitude is only ever expressed in acts less than full martyrdom.
With the Holy Innocents, on the other hand, we seem to have a somewhat different situation. Nothing absolute prevents an infant from receiving inspired fortitude, but this is in a sense incidental to the question, since an infant is not in a position to be an instrumental agent through such an infused virtue but only, at best, an instrumental patient. Thus God is principal agent of the witness of the Holy Innocents, and the act of witness in violent death is complete, but the Holy Innocents are not agents of witness in the way Stephen and John are. Yet they are no less martyrs and saints. One importance of the Holy Innocents is that they show that the witness of martyrdom, if genuine, must be very much an act of God. (The medieval theology of the Holy Innocents ends up being more complicated than this makes it sound, because, of course, the Holy Innocents were Jewish boys who were circumcised. Circumcision already made them signs of Christ and is the anticipatory sign of baptism into Christ. Thus their witness to Christ is an expression of the covenant between God and Israel that is fulfilled in Christ. Thus they were already going to be saints -- but because of their deaths they participate in the victory of martyrs as well and merit the veneration of the Church. Contrary to what some mis-attribute to medieval theologians, they weren't bothered by the fact that unbaptized children could be saints in heaven, since this was actually easily accommodated, but puzzled by the sense in which they were martyrs. Yet they were also clear that not only are they martyrs, they are an important kind of martyr, as well; all martyrs in some sense die in the place of Christ, for instance, but the Holy Innocents are the only martyrs who literally died in the place of Christ.)
Pusey has a famous sermon, entitled, "God's glories in infants set forth in the Holy Innocents," in which he notes that one of the clear lessons of the feast is the dignity of children: even an infant may be a saint of God, a witness to truth, and a temple of the Holy Spirit; and we are not just called to life everlasting, but born to the call. And this dignity does not depend on their being able to engage in great projects or elaborate choices; it does not depend on their autonomy or their consciousness of their place in this world or their ability to attribute to their own existence some basic value; it does not depend on sophisticated cognitive capabilities or having identifiable interests. Their deaths are not merely of moral interest; their deaths are things to make a man tremble; their deaths show that their lives are infinitely precious. It is in the greatest of human deaths that we see the full greatness of human life; and in Christian terms, the greatest of human deaths is martyrdom, the victory that is most victorious, and infants can have it. Some infant boys who had no idea what was going on were martyred once; and thereby they showed that their lives were capable of being, in witness, the expression of the greatest goods in the world. The Feast of Holy Innocents is a feast that says a lot.