Medusa and Umber Hulk and probably a number of other monsters suggest that a target can avert its eyes to avoid its effects.
For example, the medusa's Petrifying Gaze:
Unless surprised, a creature can avert its eyes to avoid the saving throw at the start of its turn. If the creature does so, it can't see the medusa until the start of its next turn, when it can avert its eyes again. If the creature looks at the medusa in the meantime, it must immediately make the save.
I've scoured the books but I can't find what it means mechanically to avert one's eyes. I'm assuming it's related to partial blindness or concealment but I'm not sure. So what are all the things that happen when your eyes are averted? Can you cite the rules so that I can understand it as thoroughly as possible?