What is the "Google Update" Firefox add-on?
You might have gotten the add-on, and probably an independent "Google Updater" program as well, installed by installing one of Google's programs, such as Google Earth or Chrome. Information from Google is available here, and a rather critical discussion of the phenomenon, and a way to download the programs without the updater is available here (Obsolete).
The updater can be deactivated and uninstalled. See here (unrecoverable, dead link) for instructions from Google for uninstalling it, or here for instructions about how to seek out and vanquish every trace of it. Uninstalling the add-on from Firefox might not do much without such a measure, but by all means do that as well.
I like to get rid of this invasive malware but keep Chrome's ability to do a manual update, when I request one. To that end, delete just the plugin DLL (the name varies for sneaky reasons) which resides in the user profile folder (on Windows systems).
You can find the plugin location by opening a Firefox tab and entering about:plugins in the address input. It will list the plugin, for example, like so:
Google Update
File: C:\Documents and Settings\User Joe Bloggs\Local Settings\Application Data\Google\Update\1.3.21.99\npGoogleUpdate3.dll Version: 1.3.21.99 Google Update
(Note that the plugin must be enabled to be visible.)
Just delete that DLL and restart Firefox.
I like to use CCleaner to automatically kill this DLL. Do that by creating or adding to CCleaner's winapp2.ini file. Add a section like so:
[Google Update Firefox plugin]
LangSecRef=3026
Default=True
FileKey1=%APPDATA%\..\Local Settings\Application Data\Google\Update|*GoogleUpdate*.dll|RECURSE
FileKey2=%ProgramFiles%\Google\Update|*GoogleUpdate*.dll|RECURSE
Finally, "How To Stop Automatic Plugin Installations In Firefox" details how to fight this outrageous malarkey by Google, Microsoft, Apple/iTunes, etc.
This addon updates all Google software. It is typically installed when you install Chrome. You can disable it and manually update your Google software. You should also note you most likely have a Google Update service running, and a task scheduled to run.