All the responses have been pretty technical. So I thought I would offer a more laymen's description.
A NATCH is an award that demonstrates not only that a dog/handler team has amazing skills, but has demonstrated those skills multiple times.
A NATCH is not an easy thing to earn, especially for the first time for a dog, and doublly difficult for the first time for a human. It takes a lot of time and effort, and a lot of learning and knowledge, and a lot of training and competing. Earning a NATCH demonstrates that the dog/handler team has the commitment to succeed and the discipline to overcome obstacles in their development.
A NATCH is the product of a tremendous committment and investment. A dog has to progress through Novice, then Open, then Elite, and then continue even further at the Elite level - across 3 classes for the core NATCH.
Its a big deal for a team. Many teams have earning a NATCH as their main agility career goal. A lot of dogs never earn one. Either they couldn't overcome an issue, or maybe they didn't trial enough, or not enough trials were accessible, maybe there was an injury, or any of dozens of other reasons that prevent earning the championship. But for the dogs that do NATCH, it is a very meaningful thing to earn. It is a goal that is generally years in the making. And getting that last Q that fulfills the criteria can be very emotional.