The ending, or the 21st chapter of the book, provides closure to the book for some readers. In fact, this is the only chapter where our protagonist-narrator experiences growth, or more profoundly, personal transformation. In fact, we dare say that given his newfound discontent with violence and violent music, and interest in forging a family, Alex is all grown up. Structurally, it balances out the other two parts of the book, each with seven chapters. Thematically, it comes full-circle, starting off with the same question and description combination as chapter one in part one of the book, but closing the loop with Alex rejecting the person he was at the commencement of his journey and looking forward to a new kind of life.
That would be the easy interpretation. In the United States, and for 24 years, this 21st chapter was left out of all published versions of A Clockwork Orange. In fact, Americans were so content with the extremely open-ended ending provided by the 20th chapter that no one bothered to look on eBay for a British edition of the work. (OK, so eBay wasn't around in the 80s, but hey, same idea.) What's even more interesting is that Stanley Kubrick's famous (and forever memorialized) film adaptation of the book was modeled after the twenty-chapter version, so why is the 21st chapter even necessary?
Burgess hints at the answer to this, suggesting that politics or different regional aesthetics had something to do with leaving out the 21st chapter. Perhaps it's because the 20th chapter, with evil prancing all over the page, is sexier. Perhaps optimism as embodied by the 21st chapter is at odds with the rest of the work. We have millions of theories, as do Burgess and the publisher responsible for nixing the 21st chapter in the American edition, but at the end of the day, you'll have to decide for yourself whether you prefer it one way or the other. Just be ready to justify your opinion.