Since humans lack ability to search deep, like traditional computer chess programs (fritz, stockfish et al), they create 'strategic principles' or thumb rules (center control, development, king safety) and concepts or tricks that are applicable in vast variety of situations in different ways, such as sacrifice, rooks connected, bishop pair, specific endings e.g how to corner the king with a rook and a pawn.
I think that alpha zero has independently reinvented many such concepts (percepts and concepts) and has also learnt tons of new ones - because its knowledge was not required to be built upon human evaluation functions and the strong minmax search which always assumes the opponent is a genius.
Of course, such principles themselves conflict in some situations, that is why various opening plays and pitfalls are carefully studied - eg don't develop queen too soon.
On the other hand, humans also notice that once you lose one piece (without exchange) you weaken your forces so they are extremely careful not to lose a piece without a compensation.
I think that Alphazero's play has liberated computer chess (and human chess) from the slavish fear of losing small material and overreliance on opening books and piece values.
Alphazero games show things like the 'strategic principles' like center control, development, space, initiative are far more important if your opponent is sloppy. In other words, 'sacrifice' is not really sacrifice but trading off a piece for gain in initiative, position, directed move.
Alphago (not the zero) relied on human evaluation, but alphazero sets up the entire chain of evaluation to 'search or simulation' as a single end to end process and comes up with totally new way of playing.
If you think about it, great masters of the past like Morphy, Fischer, Kasparov have been applauded for typically this kind of -counter-intuitive- play where they are not bounded by written-on-stone evaluation by take advantage of special situations that emerge. I think alpha zero's games have such 'wow' factor to it.
Why neural networks. While computer programs that use symbolic representation and discrete search can only use 'one' way of thinking, neural networks can parallelly process situations with alternate, conflicting evaluations and flip to the more valuable view in later layers.