He means the soul as "the ghost in the machine"
The "astonishing hypothesis" of the title is simply that we are "no more than the behavior of a vast assembly of nerve cells and their associated molecules." (He really needs to add "...developing and interacting with the environment," since part of what we are can only be understood as emergent properties of our structure over time.) What he does add is that "to most people" this is "a really surprising concept." I think Crick is a little out of touch because it's not surprising to me or to any number of people I know. His view, along with my addendum, is generally considered the standard "no ghost in the machine" view of consciousness.
Consciousness, then, is what this book is really about. The "soul" in the title is meant tongue in cheek, or ironically since the idea of a soul is not amenable to scientific inquiry. Crick thinks that the best way to understand consciousness is first to understand, at the cellular/chemical level, how the brain works. He proposes to make an attack on this (he likes the military metaphor) through a study of how the brain "sees." Consequently he presents a number of optical illusions, some of which I hadn't seen before. He believes it is "hopeless to try to solve the problems of consciousness by general philosophical arguments..." (p. 19). He uses the terms "awareness" and "consciousness" "more or less interchangeably" (p. 10) which I think is good since it takes the aura of awe off the pumpkin, so to speak. Crick is not a dualist who believes there is a "mind" independent of the neurons.
Of course, from my point of view there is indeed a "mind" independent of the nerve cells; this "mind" however is an abstract construct consisting of thoughts, ideas, experiences, however vaguely and inaccurately recalled, hopes and dreams, etc. It exists "nowhere" and of course everywhere. It exists before time and after time. It is not matter or energy but information written not on the wind nor on the ether, but on the vacuum of time and space. It cannot be accessed by anyone, although I personally can access some of my own mind, again however incompletely. I like to think of this "mind" as the rationalist's soul It is information, period.
Now it may be that there is an intelligence or intelligences elsewhere in the universe with the power to access such information and to reconstruct it in some sense, perhaps able even to reconstruct the matter and energy that developed it! However this is just the sort of fanciful speculation that Crick wants to get away from.
Even before he wrote this not very readable and somewhat opaque book, there have appeared a number of excellent books on consciousness discussing what Crick thinks is the astonishing hypothesis, especially books that see consciousness as a sort of illusion developed by the evolutionary mechanism. Two very readable ones are David Darling's Zen Physics (1996) and Tor Norretranders' The User Illusion: Cutting Consciousness Down to Size (1991;1998).
Incidentally, this is the same Francis Crick, who in the early fifties, along with James D. Watson, discovered the double helix structure of the DNA molecule thereby winning a Nobel Prize and achieving fame and fortune. Watson's controversial memoir about their discovery, The Double Helix: A Personal Account of the Discovery of the Structure of DNA, is one of the most readable scientific detective stories ever written. Crick is also a prime proponent of the panspermia hypothesis about the origin of life on earth.
--Dennis Littrell, author of “Understanding Evolution and Ourselves”