The principle is usually the following: after having played a game, in the post-mortem analysis with an engine it will show an unexpected (or hidden, or sometimes even simple) move that will illustrate the idea of a well-known principle. On the other hand, sometimes it will just show an exception to a principle.
I will give examples of both cases.
The following position is from the game Colovic-Ermeni from the European Club Cup in Skopje in 2015. I am obviously winning, but during the game I had problems finding a direct win.
I spent masses of time here, played 34 Ra2 and eventually failed to win the game. I considered the natural 34 Be4 f6 but it was here that I missed (and the engine happily pointed out) the simple (or perhaps not so "simple") 35 Rd2! winning on the spot as Black cannot defend the d6-pawn.
The principle of two weaknesses on display! The one weakness is the king on h8, so Black defends it by 34...f6, and since there is no progress against it then switch to the second one - 35 Rd2. Easy to explain afterwards, isn't it?
The second example is from a classical and well-known game. It is cited as a great example of the use of the principles of two weaknesses and Capablanca did everything according to the rules.
Black can play on both wings and Capablanca follows the rule that first you build up against the first weakness (which is White's weakened queenside and the threat of ...b4) and if White manages to defend then you switch to creating a second weakness on the other flank.
Hence the game followed logically: 22...b5 23 Kf2 Ra4 24 Ke3 Rca8 (threatening ...b4) 24 Rab1.
White defended successfully so now Black switches to the kingside: 24...h6 26 Nf3 g5. Exemplary play, without a doubt.
But it is here that the engine points out a concrete flaw in Black's perfect strategy. After the unexpected 27 fg! hg 28 h4! White manages to obtain either a passed h-pawn after 28...gh or the f4-square after 28...g4 and manages to defend his kingside. What a pity that the perfect strategy had a flaw!
All this means that here we have an exception to the principle Capablanca followed. In the diagrammed position he should have started with 22...g5! before White had time to centralise his king and organise his defence there.
Needless to say this is too deep and can only be understood and learned after profound analysis. But that is how our understanding of chess broadens and deepens and we become better players. All this would have been impossible (or too damn hard) without engines.
Of course, Janowski didn't play 27 fg, missed an amazing drawing line on move 35 (try to find it!) and lost an exemplary game. In any case, if you don't know the game, I suggest you take a look. You won't regret it, as the aesthetical pleasure from Capablanca's play is very rewarding.