Eye is the name given to a large, angry eye that appears in the center of the Netherworld. It seems to be the watcher of the entire world. Dr. Filius said that Eye only appears for short bursts most of the time, however even when he's not around, Chris DeLuca's hightened senses can still sense his presence.
Upon Chris' entry into the Netherworld, Eye has begun to appear more frequently, and has taken a more direct interest. When Chris got a gem that could unlock the exit from the Netherworld, the Eye did not permit it and attempted to take Chris and the gem with his eye-beams.
Dr. Filius also theorized that Eye was only a part of a much larger being, whose eye was being projected through the dimensional boundary into the Netherworld. Eye was able to be closed by using a Paintbrush with water from Chris' Pool Ship and painting the boundaries of the eye.
It's possible that Eye is the enemy of Face, as well. (Perceptual Boundaries)