However, it's possible it might be used in a few contexts:
* Fashion or design: Someone might describe an outfit or piece of furniture as "neat but not gaudy" if they want to express that it's stylish and tasteful, without being ostentatious.
* General description: It could be used to describe anything that is attractive but not overly fancy, like a house, a car, or even a personality.
Without more context, it's difficult to pinpoint the exact origin of the phrase. It's likely a simple and common way of expressing a preference for understated elegance.