What does affiliation (for a publication) signify?
Affiliation could mean anything, or nothing at all. In most cases it doesn't mean that the organization approves or even knows of the publication beforehand. In some companies you sign a contract that lets the organization vet your public work, but not in others and not in most universities. In those companies it usually only means that they approve of the fact that you are publishing, but not necessarily of the content. There can be exceptions, however, as when you are working with sensitive information, such as trade secrets. 

When I published, I listed my employer (a university) as my affiliation, but that was for identification purposes only. I probably still would, though I'm retired. I might, instead list none or independent researcher or my DBA (Doing Business As) persona. 

I think that publishers want it almost entirely for identification purposes, nothing more. However, for some affiliations, you have a sort of implied aura that gives the editor a warm and fuzzy feeling.