Millions of years ago, before the inventions of our time, before the very fire in which we use in our homes, were the first glimpse of civilization. Man had not fully developed his posture or his brain, but the very first signs were showing. Two tribes ruled this small area in the heart of what we now call Africa. These two tribes of "man-apes" were constantly fighting with each other, the fight to survive. The story leads you to one of the tribes, with "Moon-Watcher" as one of the lead males, who wakes up one day to find a mysterious "New Rock" (Which was the black monolith.) To Moon-Watcher and his tribe, this New Rock was nothing but a rock, but to their surprise, it started taking over the bodies of the man-apes, but what it made them do was beyond the "dumb" man-apes' comprehension. The monolith taught many things to the man-apes, but perhaps the most important was to Moon-Watcher, it showed him how to hit things with other things. Now you might be thinking, why is that important? Well, with this new skill Moon-Watcher defeated the other tribe's leader, and thus a new generation of man began.
Millions of years later, a monolith is found on the moon, it sends a signal towards Saturn, and thus the Discovery is built to investigate Saturn to determine if there is life. Aboard the ship Discovery were 2 awake men, David Bowmen and Frank Poole, 4 in stasis, awaiting the the arrival of Saturn, and the Hal 9000 computer, which served as the main computer that operated most functions on the ship.
When the AE-35 Unit malfunctions twice, Dave and Frank start suspecting that something is wrong with Hal, and then Frank dies in an space pod accident while trying to replace the AE-35 Unit. Suddenly it all becomes clear and Dave knows that Hal is doing something and he has to disable him.