Think of NP-complete problems as if they were a brick wall like the red plot in the above graph. Understanding the theory behind the NP-complete complexity class means recognising intractable problems in your code – it’s like having a bomb sniffer dog when walking through a minefield.
Very helpful analogy - hadn't thought of it like that. Now I'll know whether the seemingly intractable problems in my code are only temporarily intractable due to my incompetence, or actually intractable for grander reasons :)