The Show Basic info for Ticket inside unassociated Categories, help to list out all the Ticket a specific Contact has created when accessing the Contact Details page.
When this permission is enabled, the Agent will be able to see all the list of Tickets in the Contact detail page belonging to all the Categories. However, they can only click open the specific Tickets for the Category they have access to. The other Tickets which are on Category they are not associated, they can only view it, but cannot click open it.
Here is a screenshot reference of the Contact detail page view
When the "Show basic info" access is revoked, then the Agent will not be able to see the Ticket basic details at all.
Kindly note that this setting only applies only on the Contact detail page.