"Spirituality" is a sufficiently vague term that it can mean almost whatever someone wants it to mean. It often, though, is a way to express the idea that one is religious but not following a specific church. See:
http://www.oxforddictionaries.com/defini.../spiritual
https://en.wikipedia.org/wiki/Spirituality
http://www.oxforddictionaries.com/defini.../spiritual
https://en.wikipedia.org/wiki/Spirituality
"A wise man ... proportions his belief to the evidence."
— David Hume, An Enquiry Concerning Human Understanding, Section X, Part I.