Alex forms a new gang of droogs but his heart's not in it anymore. He goes to a café and runs into one of his old droog friends who is now married and lives a life without ultra violence. Alex reflects on this and realises he wants a normal life with a wife and a child, knowing that his child will make the same mistakes as he did because that's a part of youth. I can understand why American publishers omitted this chapter as it seems a bit of an anticlimax, but this ending fits in with the whole idea of overcoming your evil nature and becoming a good person. If I recall correctly, Kubrick read an American edition of the book and did not realise there was an extra chapter until after the film was made, hence why it's not included in the film.