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 CSS file.

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.

In order to create modular style sheets that are not dependent on the absolute location of a resource, authors may use relative URIs. Relative URIs (as defined in [RFC3986]) are resolved to full URIs using a base URI. RFC 3986, section 5, defines the normative algorithm for this process. For CSS style sheets, the base URI is that of the style sheet, not that of the source document.

For example, suppose the following rule:

body { background: url("yellow") }

is located in a style sheet designated by the URI:

http://www.example.org/style/basic.css

The background of the source document's BODY will be tiled with whatever image is described by the resource designated by the URI

http://www.example.org/style/yellow

User agents may vary in how they handle invalid URIs or URIs that designate unavailable or inapplicable resources.

Taken from the CSS 2.1 spec.

For CSS style sheets, the base URI is that of the style sheet, not that of the source document.

(Anything else would be broken, IMNSHO)