Personal links are links that are only visible to the user who created them. With this feature users could create their own list of links, for example their favourite pages within the site. Where this would be particularly useful is in large intranet sites, where the user needs to get to particular pages on a daily basis.
The "personal links" mode would be enabled & disabled at the module instance level, preferably within the module settings page. If "personal links" mode was off, the module would behave in the standard way.
I think this would be a simple enhancement to program. If "personal links" mode was on, the stored procedure that retrieves the links would just be passed the UserID and would match Links.CreatedByUser to this UserID.