Abraham Maslow originally described the concept of a "peak experience" as an "...overwhelming sense of pleasure, euphoria or joy, a deep sense of wonder or awe, feeling in harmony or at one with the universe, altered percepts of time and/or space, a deep feeling of love, greater awareness of beauty or appreciation, and a sense that it would be difficult or impossible to describe adequately in words."
Many years ago, when I was a JW serving the Organization, I would have described my moments of the above as "spirituality".
Now, all I need to do to feel the same way is look through a telescope at Jupiter, kiss my girlfriend, or watch "Superman: The Movie". I feel basically the same thing today but I no longer use the word "spiritual". Maybe simply "awesome" says it all without needing to add any supernatural baggage. My feelings didn't change, but I now attribute those feelings to how Nature works and how wonderfully (and flawed) my brain is wired.