What is this concept, in your opinion? How is it defined?

I think for most people it's defined as, "Y'know, marriage, duh." Which definition is of course slightly different for everybody and wildly different for many, which is of course part of the problem. I could try to define what I mean by it, or what I think somebody else means by it, or what some hypothetical category archetype means by it, but none of those definitions is likely to be particularly useful to you except possibly in defining the space of things people mean by it, which I expect you know roughly as well as I do and probably better in certain directions.

Like the one lignota cites below? Or did you have others in mind, too?

Actually I meant the one alaria_lyon cites above, though lignota's is another. Your proposal includes, '"marriage" being reserved for religious institutions,' and some people (probably including me if I cared more) would say, "no, I'm fine with saying the government doesn't get to define marriage, but neither do religious institutions."

I do think gay atheists should be able to get married, for example, not just partnered or united or whatever.