What does it really mean?

This is a matter of etiquette, rather than rules.  Click on the "More Info" button for explanations of the different levels.  This shows what level of roleplay is expected at each scene.  The more public the place, the more you should conform to what your characters can actually do, with the tools at hand, or things shown in the scene.  Failure to conform might change what people think about you, and reputation in this game is sorta the whole point....  Worst thing that can happen is -- Public Humiliation.  At any rate, the point is to have fun!

The reality requirement is something that makes sure what is in your mind is not only there...Well, I say that to simplify matters, because something may be only in your head and yet it's recognizable by others. Love, for example, has unique forms in each of our minds, but we can still determine whether someone is in love or not, which means love is real... Wait, can we really determine that?

Hmm, let's leave this for people with free time. Point is, there is a reality that we can all share, in the sense that we can sense it and make sense of it in the same way. A silky cloth feels silky and that cannot be disputed, a character having a water bucket and 5000 water on him can say he's off to 'gather more water'. A character who thinks he's a burger will have to face reality when everybody tells him to go take a nap. Your fantasy must be approved by others, because sharing is the way to make that fantasy 'real'. When all the people (or most) in a scene 'feel' the world the same way, the world is as they claim it to be.

At least, that's the theory. It sounds like a really fun adventure - to make your fantasies true - but there is a problem: those no good down-to-earth nay-sayers who're always like 'no, that is NOT true. I don't own you 10 gold coins and you are not the handsomest around'!