I find myself surprised that I never really attempted to answer this question before, nor would have been able to answer this question simply put.
According to Fr. Robert Barron, who refers to Blessed John Henry Newman's own answer, the Catholic "thing" is the Incarnation!
That makes sense to me, but I'm amazed and surprised and delighted at the answer. Here's a little of what Fr. Barron has to say about this:
I stand with Blessed John Henry Newman who said that the great principle of Catholicism is the Incarnation, the enfleshment of God. What do I mean by this I mean, the Word of God - the mind by which the whole universe came to be - did not remain sequestered in heaven but rather entered into this ordinary world of bodies, this grubby arena of history, this compromised and tear-stained human condition of ours.
This has many ramifications, of course, (especially the Eucharist) which are breezily highlighted in this introduction. Here is just a sampling:
Essential to the Catholic mind is what I would characterize as a keen sense of the prolongation of the Incarnation throughout space and time, an extension that is made possible through the mystery of the church. Catholics see God's continued enfleshment in the oil, water, bread, imposed hands, wine, and salt of the sacraments; they appreciate it in the gestures, movements, incensations, and songs of the Liturgy; they savor it in the texts, arguments, and debates of the theologians; they sense it in the graced governance of popes and bishops; they love it in the struggles and missions of the saints; they know it in the writings of Catholic poets and in the cathedrals crafted by Catholic architects, artists and workers. In short, all of this discloses to the Catholic eye and mind the ongoing presence of the Word made flesh, namely Christ.I particularly love the idea of the many different ways that people can participate in bringing Christ to the world - most notably by manifesting Christ's love to others - by being Christ for them. This too seems like a simple and obvious concept, but I don't remember really grasping the importance and centrality of this concept until reading Pope Benedict's Encyclical, Deus Caritas Est (God is Love) just a few years ago.
So, what do you think? Does this answer satisfy you? Is it adequate? Would you put it a different way?
The Angelus prayer in a more profound way.