CO* (continental stars) are a high revenue subset of passengers that CO tracks for database marketing purposes. This is an internal program that seems to be fairly difficult to define the qualifications, but LK did acknowledge it during his Q&A session. It has also been noted that CO*s receive additional attention and courtesies, but since I am not one I can not confirm or deny it.

Try to sneak a peek at the manifest next time you are on board and waiting for the WC. They seem to be hiding it more since the program was revealed on this forum, but it is seemingly the only way to know if you have been deemed a CO*.