It's about human evolution being influenced by the aliens, who use the monolith to communicate and instruct the humans (first as apes). Once instructed, an ape (Moonwatcher) invents the first tool, a bone, which becomes a weapon - there follows killing animals and eating meat, to increase the ape's brain-power. Then the tool becomes a weapon used to murder another ape - the first murder (Cain and Abel) takes place, then the bone is tossed up into the air.
Cut to a few million years later. Spaceships and an orbiting space station. Dr. Heywood Floyd travels to the spacestation, where he is asked about "the very strange things that have been happening at Clavius", the US moonbase. He keeps this a secret an uses a false cover story about an epidemic at the base.
The truth is that an alien artefact, another monolith, has been flound on the moon near the crater Tycho. A group of US scientists goes to look at the monolith, which then emits a radio beam aimed at Jupiter.
Cut to the Jupiter mission, 18 months later. he spaceship has two astronauts, Commander Dave Bowman, the mission controller, and another astronaut, Frank Poole; alseintists in suspendo, there are 3 scientisfs in suspended animation. The spaceship is run by the supercomputer Hal, which has been programmed to behave like ahuman, to make it easier for the astronauts to communicate with it.
Big mistake. The programming comes unstuck, when Hal deliberately lies about the possible failure of a unit which is needed for sending communications to and from Earth mission control, the AE-35 unit. This is a very human thing, because it is a prediction about something that has not happened, but might happen in the future.
The astronauts do a spacewalk to take in the AE-35 unit, but can find nothing wrong with it. Also, a twin Hal computer used at Earth mission control says the onboard Hal computer (on the Jupiter spaceship) is in error predicting the fault. This should not be possible, as no Hal (9000) computer has ever distorted information or made any mistake, no matter how trivial. When asked to account for the discrepancy between the computer, Hall merely says, this must be attributable to "human error", very telling. Hal has behaved like a human.
Hal suggests replacing the AE-35 unit, so that it can fail and they can trace the error. But before that, Poole and Bowman go into a spacepod and turn off the sound, so that Hal cannot hear them speak, but Hal can lip-read. Hal learns that Poole and Bowman will deactivate Hal if the unit does not fail and it has malfunctioned.
Poole does a spacewalk with Bowman watching from the Jupiter spaceship. But Hal does a very human thing and murders Poole by using a spacepod's extensible mechanical arms and hanRAB to pull out his oxygen lead. Bowman sees Poole in spacesuit careering off into space. Bowman asks Hal what has happening. Hal says he does not have enough information, a deliberate lie, a very human thing to do, down to hits programming.
Bowman goes into a pod and goes out into space to retrieve Poole's body, but in his haste forgets to put on his space helmet (unnecessary in the pod). He recovers Poole's body and approaches to pod bay; but Hal will not open the pod bay doors. So Bowman has to enter through the emergency airlock without his helmet. He just about manages this, closing the door before he can be sucked out into space.
Bowman then disables Hal by entering its control room and using a screwdriver to pull out its circuits one by one. The massive super computer dies.
The spaceship then enters Jupiter space. Bowman sees a tape from Floyd which says that evidence of alien life has been found on the moon, with a radio signal being sent to Jupiter; hence the reason for the mission.
Bowman, in spacesuit and helmet, goes into a pod and out through the pod bay doors into space; where near Jupiter's moons, he encounters a space gate, which transfers him to an alien lanRABcape, which he is guided through until the pod emerges in a room with 18th century decor, created from part of his own memory and imagination.
In the 18th century room, Bowman ages, then is seen as a dying old man, who appears to dissolve into a capsule surrounding a large human foetus. The foetus glows and enters another monolith which appears in the room as an astrochild, the next stage of human evolution assisted by the unseen aliens.
The astrochild baby foetus then emerges as an enormous figure, almost the size of the Earth and floats in the space between the Earth and the Moon.
Couple that with massive TV/projector and a serious sound setup and things might get a bit intense.