Doing an Adam (alternatively, "going for an Adam") refers to the act of doing a topless shit.
A topless shit is only "an Adam" if you took your clothes off before going for a shit. If you were already topless beforehand, it does not count. You must also be fully topless: no vests or bras.
Doing a naked shit is sometimes called a "full Adam", although a topless shit is never called a "half Adam".
The main advantage of doing an Adam is that when you are straining on the toilet, your shirt will not get sweaty from your exertions.
Joe: Dude, where's your shirt?
Matt: Oh, I left it in the toilet.
Joe: Why did you take it off?
Matt: I was doing an Adam.
Joe: Ah, of course.