When I was looking for LGBT forums and I saw this one, I clicked its link mainly out of curiousity because of the name. Don't get me wrong - I do like this forum but I'm curious why have you chosen this name. Is that some sort of a tv show? Or is it an idiom I'm not aware of?
^^ Empty Closets is supposed to signify the goal of this site- to let LGBT+ people live "out of the closet" without fear of being harassed or bullied.
It is a reference to the phrase "coming out of the closet," meaning to acknowledge one's atypical sexual orientation (or to reveal any secret, I suppose). I imagine the phrase itself evolved from the saying "skeletons in your closet."
Yes, that's pretty much the meaning. Think about a jail with all doors opened, and the prisioners just going out of their cells... Well, the LGBT version is all LGBT folks going out of their closets/cells. It's a great image. Also not only without fear, but also pride as in 'Here I am, look at me, this is who I am', which used to be a heterosexual privilege.