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I think a lot of people got there taste of quantum mechanics by reading "The Dancing Wu Li Masters" by Gary Zukav. It presents it in a new age, mystical kind of way, which was popular at the time (1970's).
There are lots of books that try to explain quantum mechanics to non-physicists, but of the few I've read, none have really given me any sense of what it's really about (I used to be a physicist, so have done my share of courses on the subject). The problem is that it is unintuitive because the microscopic world is completely different from the macroscopic world we live in, and we have almost no hands-on experience with it. Trying to describe it using analogies we're all familiar with just doesn't work. If you really want to "understand it" as it truly is, you might have to get a beginner's textbook and work your way through the math, starting with the four axioms of quantum mechanics. I put "understand it" in quotes, because I think that I and almost all other physicists don't really understand it, we only believe it because it hasn't been disproven after decades of thorough testing.
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