Imagine you have a toy train set at home. Now, imagine that train set was much smaller than your usual train set, so the tracks were closer together. This is like a narrow-gauge railway.
Now, imagine there was a place where they needed to transport lots of heavy slate rocks from a quarry (a place where rocks are dug up from the ground) to a nearby town. But the roads were not suitable for big trucks or normal sized trains to travel on. So, they built little trains with tracks closer together and called them narrow-gauge railways.
These narrow-gauge railways were used to transport the slate rocks in small wagons, called trams, from the quarries down to the town where the rocks could be turned into things like roofs, walls or floors for buildings.
The British were really good at building these narrow-gauge railways and they used them all across the country, especially in places where it was hard to transport heavy things like slate rocks. Some of these railways became really famous and are still used today, although not for moving rocks!