I've normally heard them referred to as "bots" but I'm pretty certain that "spider" in this case is the automated process where search engines like Google systematically go through a site and all its links, like a spider crawling over its web.

It's also why people (and mods) need to be careful about what is posted. A small post, buried deep in a thread, does not mean that it will go unnoticed by search engines.

Edit: Whoops, Hacksaw beat me to it. Dang, couldn't type fast enough!