I don't ever see that. But then, you didn't share any info about your setup. However, since I'm still on Snow Leopard, my money is on you not having the same setup as me.
Anyway, have you clicked on it? Obviously, or maybe not, clicking on the one that is greyed out will do nothing. But I bet if you click on the right one, the left one will then be clickable. My guess is that you have two things open in the same app, and clicking the arrow will go to another one right away, saving you the "trouble" of going to it after bringing up a different one. I imagine the one that will be active is the one that was last active, before you minimized it.
Click away! I'd be shocked if doing so would render your Mac unusable.