At the beginning, the ancients of the human beings are shown living their daily life or current status quo until a mysterious monolith appears. This monolith had a lot of interpretations through the time about what it is or what it symbolizes. An interpretation that can largely summarize those that have been given to this object could be the unknown/different. Once the primates see the large object, some react with fear, some with curiosity to know more about it and, the most important for the plot, one of them started thinking outside the box. People follow routines, many times, following an unchangeable status quo, but, once a strange or abnormal event happens, they start to notice things they haven't noticed before like new possible accidents in a work, an alternative way to get new clients, an improvement to a culinary recipe, etc. Particulary in this movie, one primate discovered it can use tools to chase animals more easily and to have advantage over other primate groups. This represents the beginning of the endless circle of human evolution.
In the next act, it's presented how far the curiosity and ambition of human beings have reached accompanied by a magnificent cinematographic section including the shots, the classical music, the space floating objects that exist in this present, the dynamic and smooth movement between scenes etc. If seeing these special effects today still has an impact, imagine the impact it had to have inside theaters when the film was released. Returning to the plot, the goal here is to investigate about a mysterious epidemic and, also, a discovery found in the moon, which it was the monolith; and, like the first act, the reactions here were similar and, at the same time, different than the primates. With more technology, the astronauts were capable to do a deeper research about it, but the primitive insticts are not really different that the shown previously.
For the final act, the objective is to reach Jupiter in order to keep expanding the discoveries made by humanity. Once this travel begins, as in the previous act, the cinematographic section with no dialogue takes protagonism showing how far the technology progressed like the rotating sets. It should be noted that this type of special effects in particular were an innovation for the time that would inspire multiple works of science fiction such as the Star Wars franchise. Now focusing once more in the plot, something interesting happens here. During the previous acts, we saw how the curiosity and thinking outside the box made humanity progress, however, now, the technolgy have reached a point were it can do everything for human beings. In consequence, they don't need to think or analyze things. This is not far from the current times at all with the cellphones, Ipads, tablets, etc. which make people more cold, distant and dependant on the technology. Basically, acting like if they are robots. Something which is perfectly portrayed here. There are many complains with the "poor" characterization and development of the astrounats of this act, however, as it was mentioned before, this is the point of the film, this is what the film tries to warn. Now let's analyze the other main character of this part, HAL 9000. A "flawless" IA which follows the mission to take the astronauts to Jupiter and attend all their needs and doubts, at least this happened until one day there was a discussion about the secrets of the mission of going to Jupiter. After that, the IA asked the astronauts to repair an antenna, but this antenna was functioning without problems. This is where HAL started having a mental breakdown refusing to admit it made a mistake thanks to its initial programmation. So, the movie reached a point where the IA started acting like a human being and the astronauts act like IAs (robots), the big irony of this movie. It was supossed the best IAs are the ones who are closer to act like a human being, this includes have emotions closer to the human ones, so it makes sense how HAL acted from now on. The astronauts noticed HAL could be now an obstacle or a problem to complete the mission due to its flaws. So they tried to disconnect it and the IA tried to stop them to preserve its "life". At the end, to emphasize the aforementioned irony, it is observed how the astronaut begins to disconnect HAL with a cold and disinterested attitude while the AI begged for his life showing different types of emotions until his disconnection.
After that, Dave discovers a Monolith in space, and, then, he's dragged into a galactic tunnel in a Slit-scan photography style where he sees another life species which don't use the verbal communication until he reachs a bedroom. These special effects where referenced or were a inspiration in many "mindfucks" moments of several works. In the bedroom, he ages quickly and sees another monolith, and, when he tried to reach it, he basically "reincarnated" into a super fetus. Following the interpretation of Kubrick, humanity reached a point where they are rat labs of deity entities, being one of the messages (one I infered), the fact that no matter how much humanity evolves, we won't reach a status similar to a god/deity, but we can keep evolving despite that as it happened with Dave being a super human in the final scene.
The only complain I have with this movie is the pacing. There are some scenes, like the beginning of the 2nd act where the pacing is appropiate, however, there are some scenes with dialogue which could be faster.
As a final conclusion, it should be noted how well was portrayed the human evolution and the Kubrick projection on how the technology would advance and its impact in people daily lives, which its very close to the current reality, and, along with the innovative special effects, this movie gave beginning to the modern Science Fiction as we know nowadays.