Floats don't have a height so the containing div has a height of zero.
<div style="background-color:black; overflow:hidden;zoom:1" onmouseover="this.bgColor='white'">
<div style="float:left">hello</div>
<div style="float:right">world</div>
</div>
overflow:hidden clears the float for most browsers.
zoom:1 clears the float for IE.