The distinction between the sacred and the profane is one of the foundational conceptual pairs of the modern study of religion, and it was proposed by two major theorists as the essential feature of religion itself.
Emile Durkheim, in The Elementary Forms of Religious Life (1912), defined religion as "a unified system of beliefs and practices relative to sacred things, that is to say, things set apart and forbidden". His claim is that the division of the world into two domains is universal and is the defining religious act; the two are held to be absolutely heterogeneous, and passage between them requires ritual. His further and far more contentious claim is that the sacred is society, experienced as an external and compelling force, so that in worshipping the sacred a group worships itself, which would explain why the sacred is felt as at once greater than the individual and internal to them. The mechanism he proposes is "collective effervescence", the heightened state generated by assembly.
Rudolf Otto, in The Idea of the Holy (1917), approached the same territory from the opposite direction, treating the holy as a category sui generis, irreducible to anything social or moral. He coined "numinous" for the specifically religious quality of experience and characterised it as mysterium tremendum et fascinans, a mystery that both terrifies and attracts, before which one feels one's own nothingness. Where Durkheim explains the sacred, Otto insists that it cannot be explained without being explained away.
Mircea Eliade combined elements of both and made the pair the organising axis of his work, treating the sacred as manifesting itself in hierophanies and as structuring religious space and time around them.
The distinction has been criticised on several grounds. Ethnographers have found that the sacred-profane division is neither as universal nor as absolute as Durkheim claimed, and that many traditions do not draw it as a binary at all. Durkheim's reduction of the sacred to society is widely regarded as unfalsifiable and as a case of explaining a phenomenon by identifying it with something else. Otto's account is criticised for privatising religion into a category of feeling and for taking a specifically Protestant and post-Kantian conception of experience as universal. And Jonathan Z. Smith argued that "sacred" is not a substantive quality at all but a term of relation, marking how something is attended to rather than what it is, a position that has become widely influential.
What remains is a genuinely useful descriptive observation: religious traditions do commonly set some things apart, do guard the boundary carefully, and do react to its violation with an intensity out of all proportion to any material loss. Whether that observation names the essence of religion or merely a very common feature of it is precisely what a century of argument has been about.