Extend Record Access:

If you have a private sharing model for any object(s) related to Case, this setting will give Case Merge Premium visibility and the ability to manipulate data within the context of the merge. 

If you do not select this option, you may see "Top level error: System.DmlException - Delete failed." logged on the primary case when you attempt to merge objects that users have limited object-level (CRUD) access to. Objects not visible to the user will not be merged. This issue is explained in more depth in the following knowledge article.