The concept of worldliness goes back over 100 years in Catholic speech. During the time in between, we have had industrialization and urbanization that has transformed the lives of many Catholics, taking them away from agrarian environs and making never-before-seen technology an integral part of daily life. Bishop Williamson is fond of encouraging Catholics to return to natural ways of living, to get rid of the T.V. and Internet (except perhaps for the watching his videos!?), and to form lives closer to the earth as our ancestors lived, for their faith was proportionately stronger, and he is convinced there is a reason for that to be the case.
It's not a stretch to say that average people today live lives of comfort and convenience that kings of past ages could only have dreamed of. Consequently, what would have been considered worldly and therefore a deterrent to virtue 100 years ago might be thought of today as nothing unusual and no obstacle to holiness.
I saw in a book from the late 19th century a message handwritten in the front pages, saying that a priest (by name) who gave (the author of the message) the book was a very good priest, a holy priest; "He was in the world but not of the world."
This descriptive phrase "in the world but not of the world" was in common usage at the time, words of admiration meant to compliment a priest and to bless his ministry. It was a way of saying the priest was not worldly. There was hardly any short sentence that could be a higher praise for any priest in those days. It was based on the concept that virtue and holiness in a priest is increased by his detachment from the world, insofar as he did not indulge himself with personal admiration of material things, such as clothes, machines, Jєωelry, fine food, wine, cigars; or personal friendships and the mundane admiration of his contemporaries (popularity).
We can look to examples of the saints (traditional saints) for understanding of this. St. Benedict comes to mind immediately. When he first began his monastic journey, the first monks who he gathered to start his first monastery gradually conspired against him because they thought his Rule (which eventually would become a monument of tradition which many other rules would imitate in the future) was far too strict. Therefore they plotted his demise, giving him poisoned bread and poisoned wine (curious choice of medium, reminiscent of the materials used for Mass in the Blessed Sacrament) to consume. They were overcome with awe when Benedict blessed the bread, for a bird swiftly flew in an open window, took the bread and flew out the window with it, and upon being blessed the chalice of wine was seen to erupt with the emergence of a small snake that crawled out of it and slithered away. Consequently the plan to kill him was foiled for the wine was no longer poison and the bread had disappeared. St. Benedict left that place and went on to found numerous other monasteries where his rule and strictness was not opposed.
St. Francis of Assisi also comes to mind, for his life's work was all about relying on the providence of God for survival, in a prayerful attempt to pursue holiness and virtue. His Franciscans is one of the three mendicant orders, the others being the Dominicans and the Servites.
Another saint whose labors were directed at reform of the religious community toward holiness and away from material concerns was St. Teresa of Avila who founded the discalced Carmelites (meaning they wore no shoes). Her legacy was the inspiration for St. Therese of Lisieux, who took her name in honor of St. Teresa.
In no small way, it seems to me, Vatican II was an attempt to divest the Church of this principle -- namely, the deliberate rejection of worldliness in the faithful pursuit of holiness. One of its docuмents has in the title the words, "Church in the Modern World" and contains overt appeal to Catholics to consider modernity as being no obstacle to holiness whatsoever. This theme is found elsewhere in Vat.II as well. The contrast between this approach and the one referred to with the words "In the world but not of the world" should be manifest to the reader who understands what I'm trying to say here.
It seems to me that the phrase, "in the world but not of the world" has fallen out of usage in the past century because Catholics have lost the sense of high regard for what it describes. So it comes to me as no surprise that this thread would be opened and this question asked. It's a good question! I have seen people eager to swoon over their impression of how spiritual a priest is, based on his mannerisms at the altar and during the consecration, which on the surface would seem to be a good thing. It is after all, a good thing for a priest to evoke the appearance of holiness when saying Mass. However, when the same priest finds up to a third of his sermon time for talking about cars and how much he likes one model and make compared to another, I'm sorry, all I can think about during the consecration that follows is how worldly this man's attachments must be. A sermon is no time to consume valuable moments talking about cars, or any other technology! St. John Bosco set up schools for the training of boys in printing and other industries, but he NEVER used his time at the pulpit to talk shop. He was all about the business of saving souls when he gave sermons, and the priests of his Salesian order carried on that tradition very well, I'd like to believe. Perhaps the emergence of Cardinal Tarcisio Bertone S.D.B. is an exception to the norm.