This option eliminates the situation where a file which you trashed in one folder is replaced with a copy of the same file from the folder it is synchronized with. 

With this option checked, a file which you delete, or put in the trash, in one folder will cause the corresponding file to be deleted from the other folder.

This option is available only when conflict checking is enabled; that is, when the "Don't check for conflicts" box in the Conflicts options is not checked.