Override file is a file the script uses to check for overrides to core code. The file name is coded into the core.
For example: lets say that you wanted to change some core css, you would put your custom css into a override file. That code is executed on top of the core css code. This allows users to put as much custom css as they want in the override file without worry of losing it because that file is not included in the install or updates. The user must create the file name (whatever that is) per instructions after the install.
We used override files alot for language keys.. So if someone wanted to change key 'welcome' => 'hello how are you' to 'how are you today' they would just put this in the override file
'welcome' => 'how are you today';
the core would use that custom data rather than the core language data. The same works for css, html, and some scripts even php but that is rare.
Some scripts out there dont want people touching the core files at all, so they give them the ability to use their own code and override the core code for custom work using override files.
Make sense now