Can someone translate this to English?
It's a term from computer science. I'll oversimplify it and say "NP" problems are those for which:
1) It's exceptionally difficult to compute an exact answer
and
2) It's relatively easy to check that a given answer is correct, if someone gives you such an answer
In practice it means that since it's difficult to compute exact answers, you end up using heuristics (that is, rules of thumb, guidelines, or "sounds like a good idea to me" approaches) to solve them.
Lots of optimization problems, like path planning, packing shipping containers, or figuring out how to cut parts out of plywood with the least amount of waste, tend to be classified as "NP."
For example, if you want to visit every state capital in the US by driving the least distance possible, and you're starting from Orlando, there are 50! (pronounced "50 factorial"), something around 3,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 possible ways to visit those capitals.
It would take too long for even really fast computers to get that exact answer. So you start with a heuristic: Wherever I'm at now, the next capital I visit is going to be the one that's the closest drive to me. So if you're in Orlando, you go to Tallahassee first, then maybe Montgomery, Alabama, then Little Rock, and so on. This is called the "nearest neighbor" heuristic.
It turns out that "nearest neighbor" answers are generally just okay, not great, but you can figure it out where to go next really fast. And sometimes "just okay and fast" is good enough.
There are various flavors of "NP" problems. Some are recognized as more difficult than others; those are the ones called "NP-Hard."
There's more to the definitions than this, but I think that's a decent summary.
ETA: Of course, you can't drive to Hawaii. For the purposes of this discussion, the capital of Hawaii is Palm Springs, California.