What he said.
OK.
We can be spiritual without being religious. Even without having a soul. (If that turns out to be the case.) Believing that there is nothing other than the physical universe that we know through our senses does not mean that I have no spiritual side. Atheists can be spiritual people.
Spirituality is the recognition of the beauty of the universe, of yourself, and of your place in the universe.
The beauty of the universe needs no defining. Each individual sees it differently. Some see it in the aurora borealis. Others see it in the incredible precision of tens of thousands of ants making up a colony, or billions of stars making up a galaxy.
The beauty of yourself is as individual a thing as the beauty of the universe. But sometimes people need to be shown just how many ways there are to be beautiful. The beauty of J.S. Bach, Michelangelo, Baryshnikov, and Mother Teresa seem obvious. But just because these people are (arguably) the top of their fields, doesn't mean there can't be an infinite number of others of equal beauty in the same fields. The purity of the act is more important than the result.
But there are many other types of human beauty. Many of us know someone who we describe as “a wonderful person.” Their kindness, humor, and patience are beautiful.
As for our place in the universe - The definition of the universe is: Me, you, the sun, Pluto, Jupiter and its moons, the Milky Way galaxy, the star Rigel, the solar winds, the free hydrogen atoms everywhere between the stars, etc., etc., etc., etc., etc., etc., etc., etc., etc., etc., etc., etc., etc., etc., etc., etc., etc., etc., etc., etc.
Notice that you are second on the list. (At least in my ordering. Feel free to put yourself first!

)
You are part of the definition of the universe. In other words, if you never existed, the universe would be defined differently! You are just as much a part of this universe as any galaxy is. Sure, it might exist without any of us, or any star or galaxy or black hole. But it would not be the universe that we know. We are all part of the definition. And what's more, in the eyes of the unimaginably gigantic universe, the Andromeda galaxy is not much bigger than you are. Basically, you are equal to a galaxy. Not bad.
Nor is the universe defined only by this moment. You are not defined by the single instant that you are experiencing right now. Every moment of your entire lifespan must be considered as part of the definition of you. Should your entire childhood be ignored when saying who you are? Same goes for the universe. Everything that ever existed, or ever will exist in the universe's huge lifespan is part of its definition. In 1,000,000,000,000,000 years, you are still a part of the definition of the universe.
In
A Wizard of Earthsea, Urlula K. Le Guin puts it this way. After Ged, the wizard, explains to a girl that light is a great power, she asks, if it is not a secret, what other great powers there are.
"It is no secret. All power is one in source and end, I think. Years and distances, stars and candles, water and wind and wizardry, the craft in a man's hand and the wisdom in a tree's root: they all arise together. My name, and yours, and the true name of the sun, or a spring of water, or an unborn child, all are syllables of the great word that is very slowly spoken by the shining of the stars. There is no other power. No other name."
And remember Brinn telling us about
ak-Haru Kenaustin Ardenol:
"It is said that he has mastered all skill and prowess that we desire, all restraint and calm, and has become perfection. Passion and mastery like unto the poised grandeur of mountains."
This speaks of his beauty, because of the dedication and purity he gave toward his goals. His dedication and purity are as admirable as a mountain's beauty. It also says that a person is no smaller, in the grand scheme of things, than a mountain.
Even the word “holy” can be used without religious connotations. From
The Glass Bead Game, by Herman Hesse:
I suddenly realized that in the language, or at any rate in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created.