There is no word "neet." There is a word "neat." The most common meaning is tidy. "He keeps his room neat," everything is organized, there is no clutter. "Neat" can also mean a term of approval. It's informal. It suggests that something is good, in a small way. "You'll enjoy visiting Boston, it has a lot of neat things to do." It's not the greatest city in the world, your life could be complete without it, but it's a nice place to visit. "Amy came up with a neat idea the other day." It's a good idea, it's a clever idea, I like her idea... it's not a world-changing idea.

Yes, NEET means Not in Employment, Education or Training.