Rim Eye is an inflammation of the conjunctiva (the outermost layer of the eye and inner surface of the eylids). It is most commonly caused by spending an excessive amount of time sat on your sofa playing Skyrim in your underpants, usually until an ungodly hour in the morning. See Skyrimming.

Less commonly, can be caused by the conjunctiva coming into contact with fecal matter, not necessarily whilst sat on your sofa playing Skyrim in your underpants.
"My God, Geoff, look at your eyes! You look like an albino!"

"Don't worry, it's just a spot of Rim Eye. Was up til 5 this morning crafting some fine dwarven armour. My wife is leaving me."
by Rimmmmmmer January 18, 2012
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