A generalised metric is like a measuring stick, but for things that aren't necessarily straight or flat.
Imagine you have a toy car that you want to measure the distance it can travel. If you have a normal measuring stick, you can only measure how far it goes in a straight line. But what if the car can go over hills and bumps and around corners? That's where a generalised metric comes in. It can help you measure how far the car actually went over all those hills and bumps and around those corners.
Or, think about a jigsaw puzzle. You can measure how big the pieces are using a normal measuring stick, but if you want to measure the distance between the pieces, you need a generalised metric. It can help you measure how far apart the pieces really are, even if they're not in a straight line.
So, a generalised metric is a tool that helps us measure distance or size in more flexible ways, to account for shapes that aren't perfectly straight or flat.