Similar to an earmuff, but covering the eyes. Used to protect young children from viewing unsuitable material.
Person 1: Check out this pic of boobies.
Person 2: Eyemuff your five year-old son first.
The act a young child or sensitive person does when something potentially crude or inappropriate is about to be shown. The specific action is simply covering the eyes to shield the lewdness.
Dude: Yo, check out these monkey brains between my legs?
Dude's unsuspecting girlfriend: What?
Dude's Friend: You might want to Eyemuff it.
Dude's Unsuspecting GF: Eyemuffs?
Ewww gross... Though they do really look like a monkey's brain.
To cover one's eyes, usually to prevent from seeing graphic material
Cenk: We have pics of Rihanna after her beating. Eye muff the kids.