Thought I'd add this since people are having difficulty understanding what it actually means:
Basically it's a way to get a document to format in a way that wouldn't be possible using the markup that is present. A good example exists in the W3 spec:
Here is the example for a ::first-letter pseudo element
The original HTML fragment
<div>
<p>The first text.
The fictional markup after the pseudo element is applied
<div>
<p><div::first-letter><p::first-letter>T</...></...>he first text.
As you can see - the original HTML specified a div and a p, but there is no way to format the first letter using standard CSS, so the pseudo elements were added, enabling the first letter to be modified
Psuedo elements allow you to do stuff like that..