Contrary to Hardiman's explanation, the "cluck" is not achieved by a roll, as the Bluegrassers operate, nor does it require picks. The next outboard finger, I'll call it, beyond the stroking finger is kept in position to strike against the next string just after the prime frailing stroke, and the collision of that nail and next string does the job. So I've been told by authorities on Banjo-L, the banjo e-mail distribution list.
The "cluck" is a startlingly hard crack, and for some occasional pieces it can be very interesting. But if a banjoist uses it all the time, as some do, it becomes annoying to the listener. I'd like to learn it one of these days; being told in general how it's done and getting it clear how and internalizing it are different matters.
Dave Oesterreich