Language, specifically nadsat, has an important several important functions in this work. First, it works as a literary device that seeks to temporarily alienate the reader from the world of the protagonist-narrator. We are initially barred from making moral judgments of Alex and co. because we aren't sure of what they are doing; we are shielded and removed from some of Alex's brutality against others. As we toil for the first several chapters learning to decipher the language, however, we build rapport with the violent teens, and even fancy that we understand them (because we have learned their language). Second, since nadsat draws its inspirations from Russian and Cockney English, it tells us about the author's political message. In Burgess's time, Russian was a seriously repressed totalitarian state, and Alex's fictional British world is not much different. Third, as we discuss in the "Characterization" section, an individual's use of language tells us a good deal about his place, function, and role in society.
The origins of nadsat betray the political message Burgess intends to convey through its usage – that Alex's Britain is not that far off from being a totalitarian state like Russia.
Nadsat is indispensable to A Clockwork Orange as a literary device. Without it, readers would never have the opportunity to develop the requisite rapport with the protagonist to stick with him through the end.