The book's introduction, written by the author, has an explanation of the title. In it he writes the following explanation for the title. He says that the title refers to a person who
has the appearance of an organism lovely with colour and juice but is in fact only a clockwork toy to be wound up by God or the Devil or (since this is increasingly replacing both) the Almighty State.
Basically, what the title is talking about is a person that behaves like a programmed toy or machine. The person has a mechanical set of morals and is essentially a robot, yet the person is in fact an actual biological creature. The story itself shows this concept through what happens to Alex. He is a character that for all intents and purposes has no moral reservations about anything. He rapes a ten year old, for example. He then goes through a behavioral brainwashing procedure that causes him to be sick at the mere thought of violence. This changes his entire behavior pattern, and he is essentially a reformed member of society. Unfortunately, his behaviors are not his. Alex has been programmed to behave that way. He essentially is acting the part of a robot despite the fact that he is a human organism.
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.