I think pg's answer is actually a pretty decent answer for everyone except the non-specialist. I suspect most people suspect the basics are a sort of super-lispy machine where the atoms are neurons and each atom can be contained in as many lists as there are synaptic combinations of neurons which include that neuron.

But there are plenty of neuroscientists who think lisp is some sort of speech impediment. I've heard lots of theories, but smart people were probably right a long time ago and we just haven't caught up.

That said, even if the lispy sort of theory works out in the end, who cares? I mean, it's like arguing about Godel's incompleteness. No matter how profound the answer, the answer just isn't going to influence your day-to-day life that much. "nothing more than electrical signals" is about all that the vast majority of people really need to understand in order to solve their particular problems.