I'd like to expand to Jez's answer a bit. A writer would normally start with whichever description of this woman first came to his mind, and he'd add whatever came up next in apposition. I don't think any more than this could be subject to a hard rule; I believe emphasis is involved in some cases, but not all.
Bill, John, and Fiddlebumps are in a reading club. At the moment they are discussing the articles in the latest issue of Playboy. Bill's wife, Hillary, walks in. But Bill asks her to leave, because they are in deep concentration.
The writer thinks of the fact that she is Bill's wife first, probably because this connection is most relevant to what's going to happen. She doesn't do anything significant; her name might as well be left out, unless she returns later.
Bill, John, and Fiddlebumps are in a reading club. They are discussing the latest issue of Men's Health. Hillary, Bill's wife, walks in. Knowing that Bill likes to brag, she asks, "Darling, how many push-ups did you do this morning? My, I think I saw you do two whole push-ups!"
The writer thinks of her name first, probably because he wants to introduce her as a character.
However, these are just examples; there could be various reasons why one description or another comes to the writer's mind first. In fact, the order could be reversed in both examples without too much change in meaning. It depends on context.