Working fiddle
You have many typo's in your code such as mispelling background as backgroung and treating div as an ID (#div). 
CSS (with explanation to typos)
body{background: #000;}                /*backgroung (mis-spelled)*/
div{width:100px;                       /*#div (treated as ID)*/
    height:100px;
    border:1px solid black;}       
To hover over a parent tag you must compulsorily use javascript or jQuery. you may be getting doubt that why there is no css property to select the parent tag, if so, then you can go through this interesting link . To avoid parent selector concept in most of cases we can evade using positioning in CSS (check Tymek's solution).
jQuery
$(document).ready(function(){
    $("div").hover(function(){
        $(this).parent(this).css('background-color','red');
    });
    $("div").mouseleave(function(){
        $(this).parent(this).css('background-color','white');
    });
});
Assuming you are new to jQuery, give a link in head tag of HTML, something like below to make the above function work.
<script src="http://code.jquery.com/jquery-latest.min.js"
    type="text/javascript"></script>
Check this Working fiddle