Do a search here on BYC for "eye infection." WARNING! Some of the pictures are really gross. You'll find a lot of information about cleansing the eye with saline and treating with terramycin ointment. I think that's what you need to do, but I'll tag people who know more than I do.
@Wyorp Rock...
This is usually a sign of infection. In the eye itself, or in nearby tissue.
Do you see anything "weird" inside the bird's beak? Post a picture if you do.