The safe_mode are some safety guidelines that are implemented on the server in our hosting plans.
In case the safe_mode is enabled, PHP checks if the owner of the script matches with the owner of the file that will interact (UID). Where it appears that the owner is different, the script would throw an error and not continue running.
In case the safe_mode is disabled, PHP will not perform the verification of UID and will accept any file type, regardless of the owner thereof.
If you have reached this term is probably because the script you use on your website prompted the disabling of it, this is because CMS like WordPress or Joomla need that UID checking is off to carry out the installation of new plugins or add-ons.