This novel is set on the imaginary island of Pianosa during World War II, and centers on the anti-hero Captain Yossarian and his attempts to survive the fanatical lunacy of his bomber squadron's commanders long enough to get home. With the death toll rising, the quota of bombing missions required for home-leave is repeatedly increased. By pleading insanity, Yossarian hopes to find a way out until the doctor quotes the notorious "Catch-22" -- a man "would be crazy to fly more missions and sane if he didn't, but if he was sane, he had to fly them. If he flew them he was crazy and didn't have to; but if he didn't, he was sane and had to." The phrase has become a part of the American lexicon, indicating any dilemma.
(Thanks for your question - this is a very enjoyable book! -- It was one of our favorites when I was serving in Vietnam.)