Have you ever played with shapes like triangles, squares, or circles? Well, those are called polygons! A generalized n-gon is just a fancy way of talking about any type of polygon with n sides.
So, if we have a triangle, that would be called a generalized 3-gon because it has 3 sides. A square would be a generalized 4-gon because it has 4 sides.
Now, sometimes we might want to talk about a polygon that doesn't look like a regular shape, like a rectangle or a pentagon. So when we talk about a generalized n-gon, we can include any kind of polygon with any kind of angles and sides.
So, in short, if we have any kind of shape with n sides, we can call it a generalized n-gon!