Well I agree with Darth Bane about how regardless of religion, they all believe we have a higher spirit or soul of some type.

I personally think being spiritual means trying to be more connected to the world around you in an energy type of way. We are all made of energy at the core. Our nervous system is an chemical electric system, really. And, it is possible to feel the current of others. You already do this but you can learn to become more aware of it with practice.

It's an awareness that, yes, everything has a spirit and we should be aware of that. Also, it is a bit religious in that you can feel more connected to whatever faith you happen to follow. But, not the praying theological side, but the "I am connected" part of it. Like, for example, for me I feel most connected when I am out in the woods listening to the quiet, or under the stars, or near the ocean.