Really, at this point those charts are the result of millions of rounds of simulations. I mean, yeah, the fact that you'll stand on a lot of hands when the dealer has a 2-6 makes sense. And you can maybe see why when the dealer's up card is a seven, standing on 16 is probably poor strategy. But a lot of is is simply "because that's what the math says."
Deviations are definitely all about the math. For example, basic strategy, I think, says to hit a 10 vs. a 10. If the (hi lo) true count is 4+, the play is to double rather than hit. It's purely about the composition of the remaining cards and there isn't really anything to do except memorize that stuff.
If you're playing for fun, basic strategy, even with a couple of mistakes per hundred hands, you can get the house edge down to .5% - .7%, and positive variance can have you walking out with some cash in the short term. I didn't bet any money until I could do 1000 hands with 0 errors, while implementing 27 count-based deviations from basic strategy. But I'm not playing for fun.