You would need to put the CSS for the background image in your MediaWiki:Wikia.css page. So in MediaWiki:Wikia.css you would put:
.YOUR-DIV-CLASS {
background-image: url(images.wikia.com/austinallyroleplaying/images/c/c8/A&A&j.jpg);
}
And on the page where you want the div, you would put:
<div class="YOUR-DIV-CLASS">Example</div>
The reason you can't put a background-image in the style attribute is likely for security reasons, because then anyone could use code like that to open a potentially malicious URL. So if you're doing something like background-image: url(some_url);
just remember that it has to go in a MediaWiki: page.