Humans make use of the fact that the optimal solution is not necessary (or probably even desirable, given the multitude of parameters to optimize for). By heuristics we can find a good solution that is also understandable to others.
A computer can understand that an optimal solution is not always needed. There is nothing about the problem being NP complete that means the computer HAS to find the optimal solution.
Humans are capable of deriving and applying new knowledge about a problem while solving it. So when confronted with a specific NP hard problem, a human solver applies intuition and thereby restricts the solution space that must be searched significantly. These intuitive rules can be very specific to the problem. There is no good computer algorithm that can do the same combination of creating and applying rules automatically.