This the real difference between human and computer is "non-deterministic" vs deterministic. In many cases, non-deterministic is far more efficient. Turing machine cares whether a problem is solvable, but it does not care if it can be solve efficiently. Pick board game as an example, the "dumbest" way is to exhaust all possibility: for go, we are talking about 10^171 game tree over 10^361 configuration. If the Turing machine enumerates traverses through the whole game tree, that means giving any configuration, we can say, whether there is a strategy to win/draw or not. To a Turing machine, this problem is solvable, and it is end of its job.

However, this is not tractable since there is no enough resource in the universe the complete the computation. The better approach is that we can some how tell if certain branches will likely to lead to winning. There is where human to place.

Human are far more efficient in this types of "non-deterministic" approach. The brain can perform association, which gives a hint. Better trained the people are able to come up with good hints that lead to victory, but so far, no computer can ever achieve this.

NP is important because beyond NP, those problems are intractable. Even though they can be solve, but when the problem size increase a little bit, the steps require to solve the problem increase exponentially (loosely speaking). NP however, it a good hint is generated, the hints can be verified efficiently.

In general, human is not better of than computer in terms of solving problems. There are specific class of problems particularly those inherit non-deterministic in nature, human are significantly better.