The condition referred to as "Cherry Eye" gathers a lot of questions from dog owners. More often than not, dog owners have heard of the condition but aren't really sure what is going on. Great Pyrenees are not predisposed to this condition; Basset Hounds, Beagles, Boston Terriers, and Cocker Spaniels are sited as being prone. (Common Disease of Companion Animals, Alleice Summers)
We know that our dogs have a "third eyelid". We see it when they awake from sleep, and sometimes it is exposed when our dog's are sick or dehydrated. It protects the eye, and helps spread half of the fluid which keeps their eyes nice and moist. That eyelid (called the nictitating membrane) is embedded in a superficial gland. The eye can position itself in such a way that it allows this gland to prolapse (poke out).
The part of their eye closest to their nose fills with the red, swollen membrane.. and it looks like a small "cherry". It is most commonly associated with younger dogs, and there are other conditions found in older animals which can cause this appearance, such as growth of new tissues (a tumor) unrelated to cherry eye.
It's irritating to the dog, but not thought to be painful. In addition to the swelling, they will probably have teary eyes. Your veterinarian can make this diagnosis quite easily. To treat this, your vet will surgically tack down that gland back where it should be. Some dogs have the gland removed, but it is not advised unless there is a tumor present. Without the gland, their eyes cannot effectively keep the eye moist and they will have chronic dry eye. Surgery is important, because without your dog may injure the eye and compromise his vision.