So, let's talk about clans first. Clans are like big families that have lots of people in them. They all have the same last name and are related to each other in some way. In Scotland, lots of people are in clans because that's how they used to live a long time ago.
Now, some clans have something called a "coat of arms." This is like a special picture that represents the clan. It might have different colors and pictures on it, like animals or symbols.
An armigerous clan is a clan that used to have a coat of arms, but they don't anymore. Maybe they stopped using it or lost it somehow. They are still a clan, but they just don't have that special picture to represent them.