I've been unable to find any information on what this box does. The Google machine suggests no-one has ever talked about it before. Toggling it appears to make no difference to the page, so I'm at a loss for what it does and if it's best to leave it unchecked or to check it.

That checkbox says whether to show on your profile, as a collection at the top, the games you paid for. Hope this helps!

Ah, that makes sense. Thanks!