Although the plica semilunaris is not exactly a vestigial organ, since it does serve a purpose, the purpose is just a fraction of what the nictitating membrane (or "third eyelid") does for other animals. It does help lubricate the eye and provides mucus to collect foreign material and create "dry pellets" or eye boogers that also collect at the medial canthus, but unlike its more developed cousin, the nictitating membrane, it has lost its ability to retract. In fact some of the few mammals that still have a nictitating membrane, like cats and dogs, have lost most of the muscle fibers to actively retract it, which birds still have. (See Ophthalmology for the Veterinary Practitioner)