How vs why I started learning genetic algorithms (random permutations selected/promoted for picking better combinations of Hamiltonian paths for solving NP-C p

How vs why I started learning genetic algorithms (random permutations selected/promoted for picking better combinations of Hamiltonian paths for solving NP-C problems obtaining near-optimal solutions quickly) and neural networks (mainly backpropagation, using different topologies) circa 1995 (college). It was like magic: you learn how to use those techniques easily in order to solve problems. However, the why was not so evident: while in the case of genetic algorithms you can understand that in a space of solutions with many similar cost solutions could allow you to pick a "good one" easily, in the case of neural networks the idea I got was like some a "magic box" which was supposed to do some interpolation/extrapolation that effectively work like generating a convex surface for giving a "solution"/"location" for a given input. It was like you got alien technology simply to make it work for simple things, but not being able to really understand why it was working (except for trivial/small networks). Do people really understand what complex neural networks do? I.e. is still trial-error only, or are built on purpose?