The title refers to the Cockney saying "as queer as a clockwork orange". It means that something appears to be natural on the outside, but on the inside, it is actually artificial. The primary topics the novel deals with are the relationship between evil and free will, the state's role in human affairs, and what it means to be human. Alex is a naturally evil human being. The government, in attempting to control people's desires, try to rehabilitate Alex so that he chooses good over evil. Alex's attempt to be good is artificial because it isn't his true nature. A human's true nature comes from the inside. The artificial nature is forced on Alex from an outside force, the government.
It can be said that Alex was artificial (or at least partially) all along. He uses drugs (at the milk bar)to start his evenings and continues to return throughout the nights and by doing so he is altering himself. He only seems to emotionally respond to extremes like "ultra violence" and sexual abuse and most of his nefarious activities appear to him as clockwork, repetitive but necessary. Even society itself in A Clockwork Orange is described as somewhat mechanised where people live for their routines.