The Web Men know lots of stuff. If they don't know it, they'll find someone who does. And if not, they're really good at faking it. I want to include one on my site. See discussion of this in Boutell.
Counters come in several varieties.
Some concatenate HTML page pieces together to produce an HTML file with the count as regular text. Others return a dynamically created inline .GIF graphic. The count is updated each time the page is displayed or refreshed in a browser. A Java applet on the page periodically communicates with the server to get an updated count. Maybe you're a neat-freak and don't want an unneeded control taking up space, however little it may be.