This is one of those rare books that is actually surpassed by the film, but that doesn't mean Arthur C. Clarke's sci-fi classic shouldn't be read: the fact that it should be read simply shows how awesome both the film and the book are. The story is standard Clarke (man meets alien civilization, alien civilization plays coy, man gets in over his head, things get really esoteric and odd), but this is where he did it best.
In brief: a monolith shows up on earth before man has evolved, but there are monkeys around. The monolith interacts with the monkeys primitively, fostering their innate abilities and knowledge, helping them become more like people. Millions of years go by. Then, when man has reached what he believes to be the pinnacle of progress (space travel), another monolith shows up, suggesting things aren't as perfect or advanced as they seem.
So a couple of spacemen get sent to the far corner of the universe to investigate. On the way, their anthropomorphic computer HAL goes nuts and tries to kill them. The book is largely concerned with this spaceflight and the dangers presented by the defective computer, as well as all kinds of questions about the nature of man, his place in the universe, and his relationship to technology.
If this all sounds a bit odd, it is. But it's also true science fiction (as in, good science and good fiction), and has influenced just about every sci fi writer since, both the good ones and the bad ones. Clarke is a thorough-going modernist humanist, and most of his ideas are decidedly not Christian, but this is a fine book, and some of the most entertaining space drama you'll ever encounter.