In a nutshell, ems are just a ratio of the parent element's font size. So, theoretically, one can write CSS and change the font size in one place and the entire site will scale proportionally. Ems can be used for padding, margins, top, left, and other CSS properties too!
Here is a good article.
And, here is an easy test:
<html>
<head>
<style type="text/css">
/* Just change in one place (body) and the entire site will scale proportionally */
body { font-size:100px; }
p { font-size: 0.5em; }
.insideP { font-size: 0.5em; display:block; margin: 1em 0 0 0;}
</style>
</head>
<body>
Body Text
<p>
Paragraph Text
<span class="insideP">Inside P Text</span>
</p>
</body>
</html>