The way I understand neural networks to work, they are actually series of connected infinitely valued logic gates, where given a numerical input from neg infinity to positive infinity, it spits out another number from neg infinity to positive infinity that feeds into the next set of logic gates, and at the end gives you a confidence interval from 0 to 1 of whether there was a pattern match or not.

To me it's very similar to Boolean logic circuits the way I was taught those in college except that there's too many gates to configure manually so you use supervised learning to find reasonable values and an arrangement of gates that works (aka your trained neural network).

I've never heard anyone else describe it this way but this is how I like to think about it. It really has nothing to do with how the human brain or much less human mind works. That's just marketing speak.