A "wipe" or "secure delete" first overwrites a file before deleting it, so that standard file recovery tools get a blank file. The alternative he mentioned (which is harder as it requires low-level access) is to rewrite the file information so that you don't have any idea where to look. At least on older versions of Windows, all Delete actually does is erase the first character in the filename and deallocate the used blocks, which means Undelete is easy if they haven't been overwritten since.
Obviously I'd call this a feature request, as it is about something Opera doesn't currently have ... moved to the appropriate forum.