May be in general religiousness is the experience of those aspects of our reality, that are per definitionem not precisely to be defined by human reasoning alone - for example: what is beauty? what is goodness? ... - or that are not precisely to be defined by our pure three-dimensional thinking in terms of time and strict relationships of cause and effect - for example: what is matter, what is an electron, what is light, ...
If we see a sunset at the seaside, by physical and neuroscientific thinking we can EXPLAIN the causes of this experience. But at the same time we know, that those aspects, that make this experience a very, very special experience for us, are not "explained" at all by all this scientific explanations alone. There are more aspects of reality beyond the "pure reason" of which the boundaries have been shown by Immanuel Kant.
And for those experiences beyond "pure reason" humanity and our cultures have artists, poets, musicians, dancers, architects and so on, who try to give valid testimonies of this area of experiences of humans. But often they are not proud because of that. Beethoven for example says:
"The true artist has no pride; unhappily he sees that Art has no bounds. Obscurely he feels how far away he is from his aim, and even while others may be admiring him, he mourns his failure to attain that end which his better genius illumines like a distant sun."
Other human beings, fascinated by the great things, that human artists can produce, like to imitate them WITHOUT having talent for that or without having discipline for that or humility or whatever is necessary to produce great and valid art. They use the wrong tools to give valid expressions of these experiences, they have unpure motivations for speaking about these areas beyond pure reason. And most badly: They use their strict three-dimensional, time- and causality-thinking to give testimonies about areas of human experiences, about that no valid testimonies can be given by this tools and methods (as we know since Kant).
Often their motivations are very "unpure". They see, that they can gain power, influence and prestige by speaking about that areas. - And this was the time, when tribal religions and world-religions came into being.
My impression is: Those "religions", that have the most resemblance to the area of arts, that have a lot of beauty in their (often childlike) phantasies and mythologies, that have a lot of humanitarianism, kindness in their thinking, give a better and more valid expression about the area beyond "pure reason" than those religions, that are predominant today.
The more humankind has gained true scientific insights, the more religion has tried to give testimonies LIKE science and its three-dimensional thinking and the more it lost its ability to give true and valid testimonies of the area, human religiousness comes from.
Modern world religions are only a very last (and bad) phase of all those human religiousness, that is possible. And in general the arts have better tools to give expression of modern "religiousness" than monotheistic religious communities of today.
And if we ask: What makes human experiences (beyond pure reason) "special", I think one often forgotten answer is: "personality". It is the fact, that each human being is unique. If your life comes to an end, one unique possibility of human experience comes to an end.