What does "religious" mean?
I don't like it one bit when folks recite the dictionary definition when addressing a question like this.
What's this like? Where "mean" is a larger question than in what way can we use the subject of our inquiry in a sentence. In that slim regard, the 1967 Merriam W. suggests that 'religious' "relates to the divine or that held to be of ultimate importance." He regards his atheism in a religious way.
And the commonly thought antonym, "secular," refers to a subject that relates "to worldly or temporal concerns"...(and confusingly), not "overtly or specifically religious." He secularly complained of an empty stomach.

But sentences other than my examples are more familiar: I know him, he's very religious. Religious protesters stood outside the courthouse today. The poll shows that most Americans consider themselves religious. We need to put religion back in the classroom. Classrooms are becoming almost exclusively secular. Secular humanism pervades the academy. I know him, he's a secularist.

What do those sentences mean?

The meaning of 'religious' will depend on the context in which it is used, and the shared assumptions of hearers. But what are our societal, generalized assumptions. More specifically, must there be a correlation between belief and action to be 'religious?'
For instance, if I believe in a truth in regards to ultimate reality (say, in a particularized notion that afterlife is achieved only if I have abstained from wine); but I drink wine with every meal, am I religious?

The questions can go on; but here's my conclusion:
Society uses 'religious' fairly openly. This contrasts with what I'll call conclusive words. If I say, "John is caucasion," there is little doubt what I mean. Of course, context is required- but the term white is fairly self explanatory. If I say "John is religious," even within context, the answer is up for grabs. Even if the question is "Is John Baptist?" the answer is open ended. "Religious" requires further inquiry. Maybe it should be called an open-ended word.
Society sometimes accepts that; but it seems we often use the word conclusively. For instance, if I make the claim, "I am religious," I might know perfectly well what I mean (of course, I also might not). A reader may happen upon this page and, while not knowing my particular dogma, assume there is one to which I subscribe, that I attend regular services, and generally gear my life to that religion. Another visitor may figure "religious" means something akin to "spiritual," whatever that means (here- I mean the 'i believe something's out there, and i don't think it matters what it is as long as we're all cool to each other kind of spiritual). Another, more frequent reader may wonder how I can call myself "religious" and also call myself "agnostic." ( ah yes, another word with assumed and unknown meanings).

As it turns out, I use religious as loosely as the next guy. But if I turn the word to describe myself, I mean to say this: I am religious. I concern myself with the search for truths, and I figure that such truths exist. I don't, however, know those truths. In that regard I'm agnostic--without knowledge. I am also pretty sure that, even if I decide I know a truth, I cannot verify in any sure way with any other person that we 1) share the same idea of truth, or 2) that my conclusion is more or less verifiable. For this reason, I dig the postmoderns.

For the agnostic bit, please see my post from September 4.

P.S.
ah yes, this may be important- though I don't know the extent to which it fits in the meaning of 'religious.' I also think that the religion one is born into, to the extent they are, is the appropriate one to follow. that's a big ole discussion on its own, but it's what i'm thinking. in that regard- Christianity is the religion i take seriously.