That message appears when the version of the module currently installed (the version showing when you list the modules from the admin menu - the same version number that's stored in the database) is lower than the one in the file
modules/modulename/module.info.
Clicking on the upgrade option runs the module's upgrade routine as defined in modules/module_name/helpers/modulename_installer.php.
You cold look in that (very small) file and see the "static function upgrade($version)" function. Usually it does nothing more than update the version number in the database, if it exists at all.
I'm 95% sure it's safe to click and nothing will happen apart from making the message go away :)