The novel skewers the specific bureaucracy of the military as well as the general absurdity of the human condition. Captain John Yossarian tries to find a way out of the cycle of insanity, but is trapped by the Catch-22 of the military's rules, which makes escape impossible. It's a Sisyphean struggle that would have made the Existentialists proud.
The Answers.com summary I linked to above is pretty good, but you'd be better off reading the book, as no synopsis can do it justice. Here's the excerpt from the novel that describes the title's emblematic catch:
There was only one catch and that was Catch-22, which specified that a concern for one's safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr 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 want to he was sane and had to. Yossarian was moved very deeply by the absolute simplicity of this clause of Catch-22 and let out a respectful whistle.
"That's some catch, that Catch-22," he observed.
"It's the best there is," Doc Daneeka agreed.