Say in the example that you are unable to change the HTML source code but only provide a stylesheet. Some thoughtless person has slapped on a style directly on the element (boo!)
div { background-color: green !important }
_x000D_
<div style="background-color:red">_x000D_
<p>Take that!</p>_x000D_
</div>
_x000D_
Here, !important can override inline CSS.