I’ve heard these mystical links called many things, whether persistent, permanent or durable, but they all mean the same thing:
Your document links will be unbreakable when changing file names or moving files because the links created for sharing/linking refer to the document by an ID instead of its common name.
But for this to work you must activate a site collection feature available only on SharePoint 2016 or later, or SharePoint Online/O365.
Before activating Document ID Service feature:
After activating Document ID Service feature: