At the dawn of man, a primitive tribe lives by hunting and gathering in a desert. The tribe discovers a black monolith, which they approach and examine. The implication is that the monolith is of extraterrestrial origin, and it imparts the knowledge of tools on members of the tribe. After the discovery, one of the tribe members scavenges a bone from a pile and uses it as a club, discovering the first tool. This tool is used to hunt, and eventually as a weapon to kill a member of a rival tribe.
After millions of years of evolution, where mankind uses the knowledge of tools to conquer the environment, and then space, a space plane carries a scientist, Dr. Floyd, to a space station orbiting earth. He is headed to an excavation on the moon where engineers have discovered a buried monolith. After he arrives, he and a team of engineers approach the monolith. As they approach, the rays of the sun strike the monolith, which then emits a high-frequency transmission. The only possible reason for a solar-powered transmitter to be buried underground is as a warning or signal of when it is unearthed.
The destination of the transmission was determined to be Jupiter. Mankind then undertakes an expedition to discover the destination of the lunar transmission. Eighteen months later, a spaceship is headed to Jupiter. Five scientists are aboard, none of whom know the exact purpose of their mission. The ship is controlled by an artificially intelligent supercomputer, HAL, which is treated as a sixth member of the crew by the other five. During the trip, HAL claims to detect an impending hardware failure in the ship's communications system. Two scientists, Dave Bowman and Frank Poole, replace the component, but find no fault in it. They are concerned about HAL's reliability, so they meet in secret and agree that if the component does not fail, they will disconnect HAL. HAL is faulty, and is endangering their lives and their mission. However, because HAL is an essential member of the team, this eventuality is problematic. Unknown to the astronauts, HAL reads their lips and discovers their plot to disconnect him. In his state of insanity, he conspires against the astronauts.
HAL is often seen as malicious. However, in truth, he was told both to tell the astronauts everything and to conceal their true mission. It was the cognitive dissidence brought about by these two conflicting orders that caused his insanity, a result that was unforseen by his designers and programmers. (That is only if one believes the sequel is an accurate source for answers of the original.)
Poole leaves the ship to restore the original communications component as planned, but HAL takes control of an empty pod and slams it into Poole, killing him. Bowman exits the ship in an attempt to rescue Poole. While he is outside, HAL cuts off life support in the ship, killing the other three scientists. When Bowman returns to the ship, HAL refuses to open the bay doors, asserting that he cannot allow Bowman to endanger the mission by deactivating him. Bowman then uses explosive bolts on the pod's hatch to propel him into the ship's airlock, and closes it before he is exposed to the vacuum long enough to kill him.
Inside the ship, HAL pleads Bowman not to disconnect him. As Bowman enters HAL's Logic Memory Center and begins extracting control chips. In one of the most famous sequences of the movie, HAL gradually regresses as his mind is taken apart until he is finally shut down. Afterwards, a video briefing plays, revealing the true nature of the mission, which is to investigate the destination of the lunar transmission. Bowman continues to the transmission destination, which turns out to be yet another monolith. Bowman descends into the monolith, and travels across space and time, passing through tunnels of light and sound, crossing an alien landscape. He then arrives in an ornate hermetic room, where he finds himself rapidly aging. He then finds himself lying on his deathbed, at the foot of another monolith. He then transforms into the "star child", a being that resembles a fetus encased in an orb of light. This being then orbits Earth, and gazes down at it. As the newly evolved star-child of the human race, he is trying to decide what to do next.