I'll share what I think it means. First, in the words of "God" as channeled by Neale Donald Walsch in the his book, Conversations with God, that was the first yellow brick in my golden road to awakening:

“Religion cannot stand Spirituality. It cannot abide it. For Spirituality may bring you to a different conclusion than a particular religion — and this no known religion can tolerate. Religion encourages you to explore the thoughts of others and accept them as your own. Spirituality invites you to toss away the thoughts of others and come up with your own.”

And now some words of my own found in my essay, https://medium.com/illumination/spirituality-redefined-ff45cb53eaf2:

"When I use the term spiritual, I use it in a manner that transcends the binary of theism versus atheism. One can act entirely spiritual with or without a belief in “god” however one understands that term. Spirituality only requires love, empathy, compassion, humility, honesty and courage.

As I define spirituality, there is a flip side to the coin and all those positive feelings— accountability, both personally and holding others accountable for their words and deeds."