A somewhat derogatory term for a gay man who has not yet come out, but is still very flamboyant. The basic terminology hinges on the idea that, while a regular closet likely has a door or curtain of some sort that would be difficult to see through, everyone can see exactly what is going on on the inside of a transparent closet.
Usage is typically snarky, following some form of "Him? Oh, he's trapped in a transparent closet," or some similar phrasing.
Again, this is a derogatory term. Just like with other words1, use of this term if you are not gay is, at least, heavily frowned upon. All I can suggest is that one checks their privilege2 and moves on.
1: Re: Queer (which may or may not be an example, depending on who you ask), fag, closet case, etc. The obscenely offensive writeup in nigger also tackles this issue.
2: Meaning remember that you come to any situation not identical to yours with certain advantages which you need to keep in mind when trying to understand why certain behaviors are taboo for you.