Going only on what's on the screen, this question may be impossible to answer without resorting to interpretation, and there are many interpretations of the ending of 2001.
While the novel, developed by <PERSON> and <PERSON> at the same time as the film, is more straightforward than the film, several events are different than in the film, so the film needs to be interpreted on its own. I'm excluding things that were explained in the book for that reason:
I think it's fairly clear in the film that the monolith that appeared at the dawn of Man either affected the primates by causing them to use tools, or was there to witness the beginning of tool use. This is symbolized by the bone that is thrown in the air, before a match-cut to a satellite.
When another monolith is discovered on the moon (the first one, as far as the human race knows at the time), a ship is sent to Jupiter to follow the transmission that the Tycho monolith (the one found on the moon) sent in that direction. Did the monolith cause the trip or hasten it? We really don't know, although the fact that we got a ship launched within a couple of years after the Tycho event hints at a mission that was already in the planning stages.
The story made a clear point of showing <PERSON> re-entering the ship without a helmet, immediately prior to disconnecting <PERSON>, his last remaining co-shipmate. <PERSON>'s final act is to trigger a recording that explains the real reason behind the mission: to investigate the Jupiter system, to find what the Tycho monolith was transmitting towards. <PERSON> has, in effect, cut himself off from all immediate contact. Despite his desperate attempt to rescue <PERSON>, he is all alone, without even a computer for company.
What we know about the events in the last act of the film, "Jupiter and Beyond the Infinite":
* <PERSON> is all alone on the Discovery, and exits the ship in a pod. 45
This same type of vehicle killed <PERSON>, and <PERSON> used one of them to survive.
* He approaches the Jupiter monolith, and is subjected to an experience that draws him away from Jupiter. He may (or may not) have been brought to other planets, star clusters, and galaxies.
* <PERSON> and the Pod are suddenly no longer in space, but in an ornate room; <PERSON> is shaken severely, possibly in shock.
* <PERSON> ages, experiencing the rest of his quiet, calm life in this suite of rooms. (He may experience this himself or see it happening from the outside. This aging may happen in the time it takes for a human being, or it may be sped-up. The film is ambiguous on these points, as on many others. Not to veer too closely to interpretation here, but note that viewpoints are a theme running throughout the film.)
* The monolith appears in <PERSON>'s room as he dies, and it either witnesses or causes his transfiguration into an embryo. The embryo leaves the room for space.
So, the story is unclear on what exactly happened. Did the monoliths cause all of these events, or simply witness them, possibly knowing that they would happen? Over how much time does the final act take place?
Both <PERSON> and <PERSON> seem to enjoy narratives that answer questions with other, grander questions. 569