These make part of an element behave like it is an element.  The simplest example are the first-line and first-letter pseudo-elements.

Open quotes.html and save it as firstletter.html.  In the embedded styles add a new rule:

blockquote::first-letter {
    color:blue;
    font-weight:bold;
}

Try it.  Change it to first-line and try it again.

There are other pseudo-elements but it is harder to find a use for them.