The book Quantum Enigma strives to explain this bizarre connection, and indeed it explains well the strangeness of the quantum world. The main focus of the book is the enigma of the title. In essence the enigma is that observation causes a particular quantum actuality to be defined from many possibilities - observation of reality causes reality. If you have ever heard of collapsing waveforms, this is where the enigma originates.
In practicality, most physicists simply accept this to be the way things work (it is), but do not question the greater philosophical implications of an observer created reality. The authors describe this as the skeleton in the closet of modern physics. The main philosophical implication that is implied (but not directly stated) in the book is that physics can prove whether or not free will exists - a staggeringly important question for humanity.
Beyond the enigma itself, the connection between consciousness and the quantum world is not so well described, primarily because there is no satisfactory scientific explanation of what exactly is consciousness. This isn't a fault of the writers who should be applauded for both their cautiousness and their decision to cover many possible definitions of consciousness.
Consciousness is almost a taboo subject to study objectively. Some people believe that consciousness emerges from the electrochemical behavior of the brain, while many others believe that consciousness and the mind are whole phenomena that cannot be reduced to smaller component phenomena. After millennia of the widely held belief that consciousness is the physical manifestation of the soul, it is no wonder that this subject is almost untouchable.
The book also serves as a well argued rebuttal to the film "What the Bleep Do We Know?!", which while introducing many people to quantum physics, is reviled in many corners of the scientific community for being too liberal in its inclusion of metaphysics as coequal to physics in explaining the weirdness of quantum reality.
Overall, the book is a good read, but as I have a computer science bias and am unsatisfied with any definition of consciousness that does not thoroughly address information processing, I recommend reading the book Programming the Universe as a complement to Quantum Enigma. Programming the Universe doesn't focus on the enigma, but rather the role that information plays in defining reality.
Quantum Enigma was written by Bruce Rosenblum and Fred Kuttner, both physicists at the University of California, Santa Cruz.
