Part of
The Odyssey That Is the Monolith, In Two Parts (read the explanation there before this!)
In 2001: A Space Odyssey, the "monolith," as it is known, is a representation of man's fear and desire to advance technologically and biologically to the future in the field of intelligence. Each encounter with the monolith brings about an extreme point of change for the human race, be it in the area of technological advancement or biological advancement, because of shifting technology.
In the beginning, the human ancestor animals (assumed to be apes of some sort) exhibit the complete lack of knowledge of technology. In such a primitive setting there is little potential for technology, what with the desolate area and seemingly only two species of animals. However, the black monolith appears, and everything is instantly changed. The ape-things almost riot at its appearance and approach it with awe and wonder. The monolith is either a timeline marker that foreshadows an extreme change, or the actual cosmic force that produces the change itself. The monolith shows this same pseudo-purpose throughout, and as a result can be either entity. The next event, whether an action or result of the monolith, is a realization of the bone as a tool, and thus the first (in this world) practical application of the idea of technology.
What can be assumed after this tool discovery is the entire progression of the human race from the ape-things to space exploration. This is explicitly shown through the transition of the flying bone to the spacecraft. The timeline jumps forward millions of years (in appearance) to man's discovery of something on the moon. The actions of the humans are extremely different than those of the ape-things, probably to show in a frank sense the changes that have taken place to modify the primitive brain to the intelligence of the modern human. The technology also seems to follow the same timeline, although it appears a little advanced (most likely thanks to Arthur C. Clarke) for the rest of the world. Once again, the monolith appears, and it can be assumed once again that it will mark an extreme change or bring one about. This time astronauts approach the monolith, with their man-made suits that serve as protective abstraction layers from the vacuum of space. At the first touch of the monolith a piercing sound is made that lasts forever. This sound can represent the insertion of the innovation that will pave the way to artificial intelligence into the human mind.
Another time period passes. In this next period, where the most remembered sequences exist, Dave is introduced. Dave is the first real peering into the true meaning of the monolith encounters. With the last encounter leading apparently to the discovery (invention?) of artificial intelligence, another important character can now be introduced as well. The HAL 9000 is the most advanced technological acheivement of the entire history of the human species. Apparent absolute sentience was the driving force behing HAL, and discussions rage on whether or not HAL was actually sentient, whether or not HAL had feelings, etc. The focus here, however, is the monolith. The drama that plays out is not a very significant part of the timeline of the monolith, but leads into the monolith's last major appearance very appropriately. This final appearance is the talk of experts, the wonder of the ages, the question that drives the intrigue that is 2001.
After this last appearance the entire story takes a turn to abstract ideas. The result is an artistic and beautiful speculation of the next level of intelligence after artificial intelligence. What follows can almost not be interpreted because of the fact that it is just so different and pliable. Interpretations over the years of what the final sequences of 2001 really are supposed to mean are the reason the film is so timeless. The best method perhaps is simply to accept your own interpretation, and listen to others for expansion and shared enlightenment. What do the sequences mean to you? That is surely what Stanley Kubrick had intended with his abstract display. Give it deep thought, and enjoy the wonderment in not knowing.
The monolith is a representation of the advancement of human intelligence. It serves as a marker for it (or possibly the vehicle for it); that is all. True understanding of the monolith's purpose otherwise can only be had by Arthur C. Clarke or Stanley Kubrick, who deserve to carry such a beautiful and wonderful secret with them to the grave.