Our hero, Yossarian, comes to the European theater of war in WWII Italy. He flies bombers -- B-25s, I think. We follow our hero as he meets the strange types of people you might meet in any army. People like Major Major Major Major, named by a father with a sense of humor, and enlisted in the army as a Major by a corporal with a sense of humor. Major Major was shy and retiring and didn't understand why all the paperwork he signed kept coming back to him with more paper. He eventually begins to sign it Washington Irving and it doesn't return. Sometime he signs it Irving Washington. He begins to do this after a CID (army inspector) comes around looking for the person who is signing things Washington Irving, thus spreading the behavior he is trying to quell. The supply sergeant, Milo Minderbinder, a funny-looking guy with eyes askew, ends up taking over the war (Radar O'Reilly), literally controlling the markets, and running the U.S. side like a business. Eventually he cornered the market on Egyptian cotton, which he then could not unload, and contracted his own private airforce (acquired by the supply system) to bomb U.S. troops for the Germans. They paid him because he could do it much more efficiently, and he openned his books to prove to the public that it made fiscal sense, even for the U.S., and since "everybody has a share", nobody complained. Ex-PFC Wintergreen controls the Allied side of the war by seruptitiously destroying, at seeming random, Allied communiques. Someday he hopes to make ex-general. Colonel Cathcart is Yossarian's boss. He is obsessed with "feathers in your cap", and "black eyes". Basically he is a lick-spittle trying to please the higher ups by continually uping the required number of missions before an aircrew can go home. And thus Cathcart is ensuring Yossarian's continued pressence (or eventual demise) in the war.
Anyhow, our hero does his bombing missions, reports on lost (and crazy) comrades, goes on sick leave trying to avoid the war, instigates the signing of documents with "Washington Irving", and generally experiences the love and life that goes on in the midst of war, along with the craziness and instability. Things change rather quickly in a war. Aquaintances come and go in many, and sometimes unsettling, ways. The disolution of reality, especially for the survivors can be either from just outliving all the familar people and things, or that the brain can only take so much carnage, and begins to get disoriented. It's hard to tell the difference from the inside or the outside.
What does Catch-22 mean? It is the repetitive, circular futility of things: war, society, government, anything. Always a no win situation, all attemps to extricate always bring you back to the original problem.