Computers play chess by number-crunching. An “engine”, as chess programs are known, slams through every legal move in a given position. Programming skills are needed to make search more efficient and ensure that evaluations are on the right lines. Fine-tuning search is hard to describe in non-mathematical terms. Improving evaluation can involve the input of "rules" set by programmers, or machine-learning techniques.
Programmers can tell an engine to look at factors like direct threats, king safety, material difference, space edge, control of open lines, piece activity, unguarded pieces, pawn structures, etc. Using machine learning techniques, the engine plays through many games until it "learns" such factors.
Computers show us how limited our powers of calculation and heuristics are. Engines almost never miss tactical stuff even in blitz, and they rarely make big positional errors. Humans can only do rudimentary calculations and apply the rules of thumb they know.
By teaching engines, we have learnt there are often hidden resources in positions that were considered "dead" in pre-computer eras. The current generation of 20-somethings and their juniors, are native engine users. The "rules" they use instinctively differ from earlier generations. "Fritz kids" are more concrete, more accurate calculators and always likely to keep looking for resources. Magnus Carlsen for example, squeezes blood from a stone because he keeps finding little ideas in "simple" setups.
Jacob Aagaard is one of the best trainers of the post-computer era. His books improve on earlier manuals by using the rules worked out in the post-computer era. His language is simple, there is little verbiage. The "rules" are stated clearly and there are hundreds of exercises to reinforce those rules. Of course, many of these rules were understood in prior eras by strong players. But average standards have improved, as average players have learnt them as well.
One of Aagaard's "rules" — try to improve the worst-placed piece. The Diagram, BLACK TO PLAY (White: Muhutdinov,Marat Vs Black: Botvinnik, Mikhail USSR 1967) is an excellent example of how this rule works. What is black's worst placed piece and how can it be improved? The first answer is the blocked Bg7. The second answer is 20.--- Ra4! (The idea is forcing e4, opening h8-a1. Even engines don't understand how strong Ra4 is). Play went 21.Rc2 e4 22.Bg2 Nexd5 23.Rfc1 Nxe3 24.fxe3 Ra7 25.Ne2 Re5 26.Nd4 Rb7 27.Nc6 Rd5 28.Qb4 h5!