The term slug comes from the newspaper/publishing business. It's a short title that's used to identify a story in progress. People interested in URL semantics started using a short, abbreviated title in their URLs. It also pays off in SEO land, as keywords in URLs add importance to a page.
Ironically, lots of websites have started place a full serialized-with-hyphens version of the titles in their URLs for strictly SEO purposes, which means the term slug no longer quite applies. This also rankles semantic purists, as many implementations just tack this serialized version of the title at the end of their URLs.