This article is from the alt.usage.english FAQ, by Mark Israel firstname.lastname@example.org with numerous contributions by others.
"Catch-22" means a trap created by mutually frustrating
regulations. It was coined by Joseph Heller in his 1961 novel
"Catch-22", which satirized military illogic. From the novel:
Yossarian looked at him soberly and tried another approach.
"Is Orr crazy?"
"He sure is," Doc Daneeka said.
"Can you ground him?"
"I sure can. But first he has to ask me to. That's part of
the rule." [...]
"And then you can ground him?" Yossarian asked.
"No. Then I can't ground him."
"You mean there's a catch?"
"Sure there's a catch," Doc Daneeka replied. "Catch-22.
Anyone who wants to get out of combat duty isn't really crazy."
[...] Yossarian [...] let out a respectful whistle. "That's
some catch, that Catch-22," he observed.
"It's the best there is," Doc Daneeka agreed.
Later in the novel, Yossarian visits a former brothel from which
soldiers have chased away all the prostitutes. Yossarian asks why.
"No reason," wailed the old woman. "No reason."
"What right did they have?"
"Catch-22. [...] Catch-22 says they have a right to do
anything we can't stop them from doing. [...] What does it
mean, Catch-22? What is Catch-22?"
"Didn't they show it to you?" Yossarian demanded, stamping
about in anger and distress. "Didn't you even make them read
"They don't have to show us Catch-22," the old woman
answered. "The law says they don't have to."
"What law says they don't have to?"
Yossarian [...] strode out of the apartment, cursing
Catch-22 vehemently as he descended the stairs, even though he
knew there was no such thing. Catch-22 did not exist, he was
positive of that, but it made no difference. What did matter
was that everyone thought it existed, and that was much worse,
for there was no object or text to ridicule or refute [...].
It is not logical for "Catch-22" to be hyphenated; other such
expressions in English normally are not. But that's the way Heller
did it. Heller originally planned to title the novel "Catch-18",
but changed it because of Leon Uris's 1961 novel "Mila 18".