apt-get update ensures your device's database is in synced with respective repository and apt-get upgrade "updates" out-of-date packages on the local device with new versions available on the repository. You'll need internet connection for this and make sure application manager is not running or apt-get will return error.

One good example is if you previously had pidgin extra plugin protocol for contacts and conversation installed, you'll notice another app called pidgin bonjour and sametime will be installed along with it. For some unknown reason bonjour and sametime will not be removed even after you uninstalled the pidgin extra plugins. apt-get update then apt-get upgrade can get rid of it.