This is the quandary of mystics, sometimes of philosophers and even of artists.
One definition that carries with it a large measure of truth is that holiness is that which is found beyond all boundaries, that which reaches absolute infinity and absolute transcendence.
And actually, our perception of holiness can be expressed by the term (used but not coined by Freud) an “oceanic feeling,” that attempts to explain or touch upon the comprehension of holiness.
A person facing the ocean for the first time, or at any other moment of heightened sensitivity, faces something grand and immeasurable, something infinite.
The feeling of “me against infinity” is, I would imagine, the basic sensation of one who stands against the holiness.
This definition is imperfect; the “oceanic feeling,” like the ocean itself, is finite.
Although it is very big, it is still limited. Our perception of infinity is, in many ways, an attempt to grasp the unlimited, the unperceivable, that which cannot be understood, that which is, in essence, the unattainable, by its very definition.
The attempt to enter the realm of holiness is paradoxical.
Because I have entered it, then, by definition, it is not truly holy; and if it is truly holy, I shall always stand outside of it.
The reply in the Torah to Moses’ prayer, his request to see the face of God, is: “You cannot see My face, for no man shall see Me and live… and you shall see My back parts, but My face shall not be seen” (Exodus 33:20-23).
This, indeed, is the point: it is impossible to see the Face; at most, we can reach an indirect, “lateral” recognition of these things, but never a direct-fundamental view.”
–Rabbi Adin Steinsaltz
From an essay titled “On Holiness and the Boundaries of Holiness,” by Rabbi Adin Steinsaltz