The feature of tracking the number of visits to each URL in your history may have been added in Firefox 3; it is stored in the places.sqlite database along with the page's URL. It appears to be used as one factor in setting the order of matches on the "AwesomeBar." I don't know if it has any other use.

As for disabling the counting, I don't see any obvious way to do that.

If you want to clear your visit count, you could erase all of your history, but I assume you don't want to do that. Perhaps there is an add-on that will allow you to reset the count to 1 for sites you have visited more than once? (I think I could write a SQL query to do it in the SQLite Manager extension, but I can't experiment with it at the moment.)

OK, thanks. I guess if there's actually a reason for it I can live with it.