The 20-20-20 rule I've heard is to stare at something 20 feet away, for 20 seconds, every 20 minutes to help reduce the strain of looking at things up close all day for those of us who need to look at things up-close for extended periods, like software developers. 

From what I understand, it works by allowing the muscles the eye uses to relax. However, I don't follow why the same can't be accomplished by just closing the eyes.

Does it not let the muscles they eye use relax? If so, why not? It seems strange to think the eyes are still straining to focus on something they can't see, or worse if they were focused on the inside of the eyelid.