A few weeks ago I started to describe what holiness means, and someone requested that I go into more detail.
One way to approach this is through the concept of the numinous, described in the classic work The Idea of the Holy by the Blessed Rudolf Otto. This book was a significant influence on St. Lewis, who discusses the numinous especially in his introduction to The Problem of Pain. The concept of the numinous is difficult to explain because most of the language we use to describe it has come to mean other things. In English, the words "awesome" and "awful" both used to mean the same thing: the feeling of dread, wonder, uncanniness, terror, or reverence one gets in the presence of something you believe to be eerie or supernatural. As Lewis points out, we use the same word "afraid" when we say that someone is a jungle is "afraid of tigers" as that someone in a haunted house is "afraid of ghosts". But in the first case, the fear is just for our own safety, whereas in the case of ghosts one is afraid of what the ghost IS, more than what it will do to you.
Please note, I am not claiming that ghosts exist, but rather using them as an example to make a point about human psychology. Just as we have a sexual instinct which responds to sexual stimuli, so we have another instinct which responds when we believe we are encountering supernatural stimuli. The hairs stand up on the back of our neck and we feel chilly. In that sense it feels like fear, even though the experience may be pleasant or unpleasant, and we may or may not be concerned for our physical safety. Atheists, pagans, and Christians all experience this feeling on certain occasions; the difference is how they interpret it.
In our own minds, we can feel numinous feelings without making any connection to ethical concepts; a pagan or a pantheist may feel that they are worshiping a Spirit which is beyond human notions of good or evil. However, when ethical concepts do intrude, a special composite feeling arises. In the case where the object is perceived as Numinous Evil, we call the feeling that arises in us Horror. This feeling can be excited by natural objects which seem "eerie" such as corpses or creepy insects. (Lewis claims that there is no survival advantage in this feeling, but it seems to me that avoiding diseased corpses and dangerous insects may well have evolutionary advantage.) It can also be excited when we read or watch movies about vampires, werewolves, demons etc. (This assumes that the movies treat the topic seriously, of course. Monsters that think and act just like regular people are humorous, since we expected a numinous thrill and then it was a false alarm).
When the object is perceived as Numinous Good, this composite idea is nothing other than the Holy. (Unfortunately, there's a lack of grammatical parallelism here, in that "Holy" refers to the Object about which we have numinous feelings, whereas "Horror" refers to the feelings themselves.) The distinctive characteristic of holiness is that ethics itself becomes imbued with supernatural significance. This experience is not always happy. As the classic example, consider Isaiah chapter 6:
In the year that King Uzziah died, I saw the Lord seated on a throne, high and exalted, and the train of his robe filled the temple. 2 Above him were seraphs [burning ones], each with six wings: With two wings they covered their faces, with two they covered their feet, and with two they were flying. 3 And they were calling to one another:
“Holy, holy, holy is YHWH of hosts;
the whole earth is full of his glory.”
4 At the sound of their voices the doorposts and thresholds shook and the temple was filled with smoke.
5 “Woe to me!” I cried. “I am ruined! For I am a man of unclean lips, and I live among a people of unclean lips, and my eyes have seen the King, YHWH of hosts.”
6 Then one of the seraphs flew to me with a live coal in his hand, which he had taken with tongs from the altar. 7 With it he touched my mouth and said, “See, this has touched your lips; your guilt is taken away and your sin atoned for.”
8 Then I heard the voice of the Lord saying, “Whom shall I send? And who will go for us?” And I said, “Here am I. Send me!”
If you are a nonreligious person, I hope you tried to read that as you would some passage in a fantasy novel, with "suspension of disbelief". Put aside how you feel about Christianity in general, and just ask how this passage makes you feel, as if it were a fictional work of art.
Doubtless Isaiah knew beforehand that he had ethical shortcomings; perhaps he lied, or berated someone. But before, it was a matter of merely personal regret, excused by the fact that everyone does it. In the presence of this astounding vision, his guilt becomes something completely different: a feeling of uncleanness and shrinking before a majestic purity, that even the angels had to hide their faces from. It was like coming into a formal dinner party stinking, and wearing no clothes at all.
This is a numinous problem, not just an ethical problem. So it needs a numinous solution. The coal from the altar makes "atonement" for Isaiah's uncleanness. That is, it allows Isaiah to become a participant in the numinous, in a way that covers up or removes his guilt. Only then can St. Isaiah hear God's call to be a prophet, denouncing the sins of others.
It's a mistake to try to argue that Christianity is true before the audience knows what Christianity is. Before people can understand Christianity, they have to understand the basic concepts in which it is expressed. Without the concept of holiness, nothing we say about God deserving worship, or about Jesus dying on the cross for our sins, or about love requiring purity—none of it makes any sense at all!