The “Delete Cached Package Files” button deletes the packages stored in the system’s package cache (`Dir::Cache::archives` and its `partial` subdirectory, typically `/var/lib/apt/cache`). These aren’t necessary for normal system use, they’re only useful if you ever need to re-install a package — they’ll save a download, or in cases where a package has been dropped from repositories, enable the re-installation which wouldn’t otherwise be possible.
(I use `apt-get autoclean` along with `APT::Clean-Installed` set to `false` to trim my package cache while still ensuring I can re-install packages; `apt-get autoclean` corresponds to the “Only delete packages which are no longer available” setting in Synaptic.)
The history files are used in the History browser in the File menu. They aren’t necessary for anything else.