What is is.
The URL of the page which contained the link for this request.
What it says.
It tells you the URL of the page where the user found (and clicked on) the link to the requested page. That could be a plain web page. Since i.e. Google ranks pages higher that have a lot of other pages linking to it (taking into account the popularity of that page as well), we should be pleased if many hits come from popular pages, indicating that well visited pages are linked to ours.
Then we have search result pages. The user called up a search machine, entered search terms, submitted the query, got the results, and clicked on a link that led to your web site. The good news is that a search led to one of your pages.
There is a wealth of information in that referer! First, the host portion tells us which search engine has been used. Second, the query parameters are encoded in the URL, and AC.log Pro can decode them (for most popular search engines). This is how AC.log Pro is able to produce reports on what and how users are searching for your pages.
Similar things apply to searches in i.e. shareware archives.
What may cause trouble.
In reality the content of the referer field completely depends on the requesting program. A browser probably indeed will send the URL of the page which contained the link the user has clicked upon. Crawlers, link checkers etc. might send nothing at all, or something entirely different.