
First things first: the significance of the title
This is what Anthony Burgess said in an interview with Rolling Stone magazine.
"The title of the book comes from an old London expression, which I first heard from a very old Cockney in 1945: 'He's as queer as a clockwork orange' (queer meaning mad...). I liked the phrase because of its yoking of tradition and surrealism, and I determined some day to use it."
In an introductory essay entitled "A Clockwork Orange Resucked," Burgess writes 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."
In other words, and again Burgess's own, it stands for the "application of a mechanistic morality to a living organism oozing with juice and sweetness."
Here is another quotation from Burgess that sums up nicely the whole issue:
The book was called A Clockwork Orange for various reasons. I had always loved the Cockney phrase 'queer as a clockwork orange', that being the queerest thing imaginable, and I had saved up the expression for years, hoping some day to use it as a title. When I began to write the book, I saw that this title would be appropriate for a story about the application of Pavlovian, or mechanical, laws to an organism which, like a fruit, was capable of colour and sweetness. But I had also served in Malaya, where the word for a human being is orang.
(From 1985, Hutchinson & Co. Ltd, London, 1978)
So, there are 3 points to made about the title's significance.
1) The phrase 'queer as a clockwork orange', that cockney slang term that Burgess liked the sound of.
2) The title sums up neatly the attempts in the book to apply a mechanistic framework on a human, or to treat a human being as a machine, a kind of immensely intricate clockwork, or as a programmable computer.
3) The word 'orang' in Malaya means man (orangutan meaning man of the forest) and there is a kind of pun on the idea of a clockwork man which of course reinforces point 2.