FYI This explanation of the Black Monoliths comes from a conversation Arthur C. Clarke had on the air with Walter Cronkite the night of the 1969 moon landing.
The film is divided into four segments. Each segment contains a black monolith. The monoliths represent extra terrestrial contact.
(I) Dawn of Man: Man-Apes and the Teaching Machine
Ancestors of man (man-apes) are visited by an extra terrestrial monolith which teaches them to use a bone as a weapon (tool). They defeat the competing man-ape tribes, turn from being hunted into hunters (top of the food chain), and become the dominate species on earth. Jump cut to:
(II) 2001: Moon base - The Alarm Bell
An magnetic anomaly is found on the moon. After excavating the site of the anomaly, a black monolith is found. It has been buried there for thousands of years by some advanced civilization. It is waiting to be discovered by man; waiting for a time when man is advanced enough to find it (the fruit of the teaching machine.) When the first rays of sunlight in thousands of years hit the monolith an ear piercing signal is sent out. Its intent is to notify the advanced civilization that man has found the monolith and is coming.
(III) 2001: - The Star Gate - (Several months later aboard a space ship heading for Jupiter)
The alarm signal has been sent towards Jupiter but this information is so classified that no one, not even the crew knows about it. The exception is the HAL 9000 computer, which knows the real mission. (BTW if you change the initials by one letter of the alphabet H A L becomes I B M) HAL essentially has a nervous breakdown because of the stress related to secrecy. When the astronauts consider shutting down HAL, he decides the mission is too important to allow this to happens and tries to kill the crew. He fails and one astronaut, Dave Bowman, survives. When HAL is turned off, a video tape is played that reveals the real mission. Dave sets out in a small space craft to investigate. He finds another monolith, the Star Gate, floating in space. This sucks him in and he is sent into a wormhole to metaphorically meet his maker.
(IV) Somewhere in the Universe: The Star Child
The end of the movie represents man's next step in evolution, the Star Child. To be reborn one must die so there is a symbolic scene of Dave growing into an old man and dying. He meets his evolutionary "maker", another black monolith, which is symbolic of an advanced civilization. Just as the first contact changed man's evolution, so does the final one. He is reborn as a giant embryo, a Star Child, with the whole world (Earth) in his hands.
BTW Cronkite asked Clarke what the advanced civilization was like. He replied that to try and describe them would be like the man-ape trying to describe modern man. It was beyond his comprehension.
Reading the book will help answer other questions you might have about the movie.