Using relative URL in CSS file, what location is it relative to?

According to W3:

Partial URLs are interpreted relative to the source of the style sheet, not relative to the document

Therefore, in answer to your question, it will be relative to /stylesheets/.

If you think about this, this makes sense, since the CSS file could be added to pages in different directories, so standardising it to the CSS file means that the URLs will work wherever the stylesheets are linked.

It's relative to the stylesheet, but I'd recommend making the URLs relative to your URL:

div#header { 
  background-image: url(/images/header-background.jpg);
}

That way, you can move your files around without needing to refactor them in the future.

It's relative to the CSS file.