Unless I'm crazy, I seem to remember a help file/thread that listed what every check box in Ccleaner did. I can't find it now though and I'd like to know exactly what the "compact databases" check box for Firefox does. I hadn't upgraded ccleaner since v2.23.999 so it's new to me plus I'd like to check on a few other things.
It has to do with the SQLdatabase that Firefox uses to store things. Over time they become larger and larger and the option to compact does just that. There are several other freeware's that do essentially the same thing such as "Speedyfox".
Urlclassifier3.sqlite came from the initial installation of FF. it is probably updated, because it is part of the FF phishing protection scheme.
"Compact" means exactly what it sounds like: Free space is squeezed out from where entries have been deleted. Same goes for any of the other databases (bookmarks, etc.). Think odf it being akin to defragmenting free space on a hard drive.
if it does the same thing as VACUUM command that mozillalinks.org suggested, and Vacuum Places Improved addons, then apparently it is not needed anymore in Firefox 4 and above.