This phrase comes from a novel by Joseph Heller. Catch-22 is set on a U.S. Army Air Force base in World War II. “Catch-22” refers to a regulation that states an airman’s request to be relieved from flight duty can only be granted if he is judged to be insane. However, anyone who does not want to fly dangerous missions is obviously sane, thus, there is no way to avoid flying the missions.
Later in the book the old woman in Rome explains that Catch-22 means "They can do whatever they want to do." This refers to the theme of the novel in which the authority figures consistently abuse their powers, leaving the consequences to those under their command.
In common speech, “catch-22” has come to describe any absurd or no-win situation.
Read more about this topic: Allusive, Examples of Allusion