You might get this folder deletion error when using Outlook 2013 when you are trying to empty your deleted items where folders are contained within the deleted items:
Cannot delete this folder. Right-click the folder, and then click Properties to check your permissions for the folder. See the folder owner or your administrator to change permissions. Outlook is synchronizing local changes made to items in this folder. You cannot remove this folder until the synchronization with the server is complete.
This is what the notification message looks like:
This is normally due to a permissions issue, where permissions are missing on the folders.
A temporary workaround to resolve this is to login to the Outlook Web Application (OWA) and empty your deleted items on there.
A fix for this would be to remove the Outlook mailbox from the computer in question and add it again, this resolves the issue every time in my experience. Obviously it would be a good idea to backup any .pst files or other metadata before doing this to reduce the chances that something is deleted that will be required by the user in the future.