Asimov had an active and brilliant imagination - truly, a scientist writing fiction. This series is science fiction on a grand scale. When you keep in mind that this story originated in 1951, it is easy to see how much Star Trek, Star Wars and yes even Heinlein's & Clarke's later works borrowed from these ideas.
Anyway, Asimov at his best was a creator; he had amazing ideas of the universe, how it worked, and how to structure stories that manipulated the readers expectations.
The Foundation series is like a spider web that continues to become more intricate and complex with each chapter. The intricacy of the plotting is amazing, although honestly it's not self-evident in the first few stories of the first novel, given that they were published independantly, as serialized short stories told one at a time.
Only with the second book did this change.
The basic premise: The rise and fall of the roman empire, told on a galactic scale from a historian living in the 2nd empire a thousand years later.
The setup: One man creates a science, called Psychohistory, a fictional precursor to Chaos Math (a real statistical science today). This psychohistorian, Hari Seldon, predicted that the vast Galactic Empire is about to crumble, dropping humanity back into the dark ages. This dark ages was due to last 30,000 years (I believe), and while it is too late to prevent this horrible breakdown of society, Seldon believes he can use this new math to shorten the time period between empires.
To do so, he establishes two "Foundations" made up of scientists, one at the outer edge of the galaxy, and the other at "Star's End". In advance, Seldon plots out the future (using the math of psychohistory), and sets in motion a series of "domino" events. The Foundation faces crises and problems, forcing change in both strategy and focus for the next several hundred years. But Asmimov continues to modulate the story throughout each of the books, and building upon the previously-understood structure.
In fact, once you think you've read enough permutations on the same idea, Asimov starts tearing the structure down, introducing variables into the story that further complicate matters.
A caveat about the most often-touted complaint about Asimov: His writing style (or lack thereof):
In 1951, when these stories were first published, Asimov was not a great writer - as in, a writer of literature. His descriptions, characterizations and storytelling technique all left a lot to be desired. His technique got better with the passing years, such that any of his fiction written after 1970 or so reads easily.
But that is not the point, here. Asimov didn't create great characters (save for his robot stories) - he came up with mind-bending ideas and subsequent permutations.
The litmus test of whether or not Asimov is for you: Read 'The Last Question'. It's a 12-page short story. Not brilliantly written, but a fantastic story with amazing ideas contained inside. When you get to the last sentence of it, you will probably be blown away. If you are, Foundation is for you.
Read them - and commit to all of them, because they get better as they go, generally speaking. The first three were written in 1950 - 53. But the fans demanded that he someday continue the story, so he continued with a fourth book in 1983, and the last in 1986. Some complain that the last book is overlong - and I agree - but the last sentence of the last book is...amazing.
Foundation and Empire
Second Foundation (contains the best story - Search By The Mule)
Foundation's Edge (best overall book)
Foundation and Earth
Afterward, Asimov went back and wrote prequel novels (Prelude to Foundation, Foundation's End) taking place prior to and concurrently with events from the first book. He later admitted that he wrote prequels because the main story had gotten so complicated, he felt he'd taken the story as far as it could go.
The prequels aren't too bad, but they are completely non-essential.