The name Catch 22 is taken from the title of the book by Joseph Heller. As far as I know there is no explanation as to how this was arrived at (why not 23?).
In short the main character wants to get out of the war by appearing mad, but anyone wanting to get out of the war must be sane, and therefore he can't be mad! Or something...
Pretty near exact. The catch is pointed out by Doc to Yossarian, a precis being: No madman can serve in the armed forces, so to get out of the forces Yossarian wants to pretend to be mad. The problem is that under regulations the mad person must ask to leave. But by army definition anyone who is sane wants to leave, so anyone asking to leave must be sane, wether they are mad or not. The net result is that madness is no way out. The only way to escape is to paddle a liferaft to Sweden.