I'm guessing here but maybe this wider idea of spirituality that escapes the paranormal stuff and connects more with what some are saying in this thread is an experience, that somehow allows us to connect with ourselves a little more, an experience that re-enforces the self maybe. Be that through a sense of comfort in your place in the world or something that makes you think or more accurately feel something deep about yourself.
I think spirituality harps back to peace and harmony between this idea of self and surroundings which Cyracuz summed up superbly for me...
Cyracuz wrote:What you believe is not the most important thing. It is where your beliefs take you that is important.
As I see it the point of any religious or spiritual quest or creed is to live well and happily. To find the balance in existence where you can be at peace and bloom. The personality and experience of each individual will determine where that balance is, and the spiritual aim is for me to move and shift along with this balance as it unfolds in the form of my day to day existence.
(I didn't post in the beliefs topic, I had too much fun reading through it, but this ^ is it for me, balance in existence)
...so these experiences that closely connect with "us", are almost pearls of wisdom that will allow us to more freely live at peace with the world, after all, if you don't understand yourself, how can you hope to understand the world and indeed, flourish within it.