This rule has been discredited. Open corners can work, brah.
I never got a straight answer about the corner thing.
The open corner rule states that when designing screens, you should always have some sort of a solid tile occupying each of the corners. If you don't follow this rule, then you're forced to open 3 corners on the adjacent screens and the screen will look a lot more "empty". But like with any good rule of art, it's mostly intended for beginnners. You can make great screens with or without open corners, but the rule is generally accepted because closed-corner screens look good more often.
But on the other hand, with art it's easy to throw out the "rules" and still make something really amazing if you have enough talent. Take colors in pixel art, for example. The general consensus is that most dark colors should be less saturated than the highlights, and you should avoid mixing warm and cool colors when shading objects. But at the same time, really experienced artists like JINN are able to, say, take the god-awful CGA palette (pure black, dirty white, oversaturated magenta and bright cyan) and make something amazing out of it. So to put it simply, if you feel you're a fantastic screen designer, open those corners. But if you're not so sure of your skill, keep em' closed to keep it safe.