Maybe I just didn't get it, but after reading Hawking's book, I'm no closer to understanding why he and others think that M-theory is so promising.

I realize we're dealing with difficult theories, but I don't have much understanding of quantum theory beyond a superficial level either, yet I have read books that at least gave me some insight into what it's all about. (Of course, I'm criticizing Hawking's book rather than the theory itself.)

M-Theory is just as hard to understand as Quantum Mechanics and it is half a century younger so there are not as many examples created to make it easier to understand. Basically it comes down to that because of the imprints left in our 4-D universe there is enough evidence that there are more dimensions (this has been shown by both the standard theory and string--this has been known for 60 years) also there are artifacts in the mathematics used every day that indicate that there are multiple universes. When you combine these bits of information you get M-theory. But it isn't a theory most people think about but a framework from standard theory, string theory and multiple universes (from the mathematics) that tells us which questions to ask next and how to put the parts that don't overlap, such as Relativity and Quantum, together so you can transfer the information from one field into another. Because it is more of a question and transfer method than a new theory that explains physical events by itself many scientists don't like it and want to find and use something better. But most of the scientists doing the very advanced work in these fields think that it is the best we can do for now. The reason is that, since quantum, scientists have started to accept that uncertainty has to be included in the advanced sciences we are not working in and M-theory is framed around the uncertainties. It is a version of the uncertainty principle but for how different theories interact.