What that usually means is the person has rejected "organized religion" in favor of the mystical, the obscure, or a syncretism of one's own creation. Sociologically speaking, there really is no distinction. Spirituality or religion is the same thing. We acknowledge something beyond the material. We reach outward to embrace the divine.
In a fascinating article written around Christmas of 2005, Umberto Eco speaks to the universality of religion.
"Human beings are religious animals. It is psychologically very hard to go through life without the justification, and the hope, provided by religion."
"It is the role of religion to provide that justification. Religions are systems of belief that enable human beings to justify their existence and which reconcile us to death."
Eco was raised Roman Catholic but has rejected the church. Still he accepts the superiority of the Christian religion. He states, "I have a profound respect for the Christian traditions." Moreover, he specifically calls the religious celebration of Christmas, "a clear and coherent absurdity."
This I would argue is the conservative position. Christianity has proven itself as a religion. It is tried and true compared to the occult and more novel beliefs. As a religion, it has a track record. It's influence in the development of Western Civilization has been on whole a positive for all humanity.
However, the Western Church is dying. Eco notes,
We in Europe have faced a fading of organised religion in recent years. Faith in the Christian churches has been declining.
The ideologies such as communism that promised to supplant religion have failed in spectacular and very public fashion. So we're all still looking for something that will reconcile each of us to the inevitability of our own death.
G K Chesterton is often credited with observing: "When a man ceases to believe in God, he doesn't believe in nothing. He believes in anything." Whoever said it - he was right. We are supposed to live in a sceptical age. In fact, we live in an age of outrageous credulity.
The "death of God", or at least the dying of the Christian God, has been accompanied by the birth of a plethora of new idols. They have multiplied like bacteria on the corpse of the Christian Church -- from strange pagan cults and sects to the silly, sub-Christian superstitions of The Da Vinci Code.
The conservative position is ultimately weak because the superiority of the Christian religion is no guarantee of it's viability. The appeal made by Eco treats Christianity as one choice among many -- granted a superior choice but still merely a choice. That argument already concedes so much. The God we Christians worship is more than a choice. He is the Lord of lords, King of kings. This God has a legitimate claim over all of our lives. If we fail to praise this God, the very rocks will cry out.
Instead, I would argue that Christianity is not a religion. This is not a new thought. Karl Barth takes this position. Religion is about our reaching upward to God. On the other hand, Christianity is about God reaching downward to us. Religion is a human work. Christianity is a divine grace.