The subject of the monoliths has been an ongoing topic for film fanatics since the first viewers walked out of the theater in the 60s. It is common to think of them as radio beacons or some kind of technology. However, there is another point of view which I encourage you to explore. In <PERSON> analysis on his Youtube channel Collative Learning (2001: A space Odyssey meaning of the monolith revealed (2014 update)) he states that he believes the monolith represents the movie screen itself. I encourage you to watch the two part analysis before making up your mind. I also encourage you to watch <PERSON>'s other movies (Shining, Eyes Wide Shut, A Clockwork Orange, and Full Metal Jacket) and then go back to 2001 to see what you think. I say this because the monoliths are really his invention. They take on a life of their own in the movie. I also think that the sequel is not worth mentioning when speaking about the monoliths. 83
The sequel is a product of later film generations who can't stand mystery and need pat answers, otherwise they feel cheated. It also wasn't a <PERSON> film.
You asked what the monoliths "do." I think a better question is "What do they represent?" I also think that to refer to the book for "source" material is not the best way to go because <PERSON> used <PERSON>'s original short story as inspiration, and in his hands, the story took on a life of it's own. This is a <PERSON> film and is filled with visual metaphors, meanings, riddles, and red herrings. He is a film genius, like <PERSON>, so the monolith is going to have several meanings and purposes (purposes for the film audience as well as the inhabitants of the universe he was creating.) <PERSON> is a kind of cinema version of <PERSON> and his films are like Finnegans Wake except more approachable.
I remember seeing 2001 on the big screen when it was released, and the thing I remember most was the monoliths. I remember most people wondering about them: How big are they? What were they made of? What do they do? What do they represent? Was <PERSON> inside the monolith at the end of the movie? Who made them? Are they time machines? Etc.
From the point of view of the characters in the movie the monoliths are devices that connect with another civilization. This is what they do. I think <PERSON> showed that in the movie quite well. However, I think the monoliths are also for us the moviegoers a representation of ourselves through a movie screen. Are they reflecting our thoughts and ideas? Are the monoliths our way of talking to ourselves and teaching ourselves ideas? Is it possible that the aliens who built these are really ourselves just a future version? There are many monoliths on our planet, some already understood, others still a question mark. Stonehenge daily reveals more secrets.
I'll finish up on this idea: Are the monoliths a reference to <PERSON>'s allegory of the cave? 663