Deprecated function in CiviEvent error logging (Drupal 7)
That message shouldn't affect your usage of CiviCRM.

A deprecated function is typically one that works, but is no longer recommended for use.  The message is only applicable to developers.

To take an example with a visible component: You may have noticed that CiviCRM has two different calendar widgets.  The older one isn't accessible to folks using screen readers (i.e. Braille or text-to-speech).  However, each date field needs to be converted separately - a lot of work!  Rather than do them all at once, we have both calendar widgets in CiviCRM, but the first is marked "deprecated" so folks are warned not to use it in new code, and to remove it from old code when they touch that section.  In time, that code will be removed - but for now, it works as it always has.

Unless you have an extension that uses this deprecated function, there's no action you need to take.  While it's unlikely you have an extension that uses this, you can double-check by searching your extensions directory for the text CRM_Event_BAO_Event::checkPermission.