Now that IS a challenge Bindeweede.
It's the explanation for all things unknown: psychic powers, homeopathy...
Seriously though, it's quite a topic (and I'm certainly no expert in this area) but there are some books that are quite a good introduction - John Gribbin. Hang on... found it.
Found it - page 1 on our Amazon bookstore: http://www.ukskeptics.com/bookstore.php
In Search of Schrodinger's Cat
I've read this book and as long as you have a rudimentary understanding of science, it's an excellent introduction.
It gives you a good basic knowledge of what it's all about. I think it begins with the double-split experiments and the dual nature of the wave/particle duality of the nature of light and goes on from there IIRC.
I've just read the review and it says that you require some mathematical knowledge too.
Does this book claim to explain quantum physics without maths? No. Maths is too central to physics to be bypassed. But if you can do basic algebra, you can understand the equations in In Search of Schrödinger's Cat.