The Hilbert metric is like a special kind of ruler that helps us measure distances in a special way. Imagine you have a map of a town and you want to know how far it is from one point to another. If you use a regular ruler, the distance will be straight from one point to the other. But if you use the Hilbert metric, the distance will twist and turn in a special way that helps us measure distances more accurately.
It's like playing a game of Squiggly Lines where you have to connect dots, but instead of making straight lines, you have to make lines that turn and twist in a special way. By doing this properly, you can measure the distances between the dots more accurately, even if they are far apart or in strange shapes.
The Hilbert metric might seem a little confusing at first, but it is actually very useful in geometry, math, and even in computer science. It's like having a secret weapon that helps us measure distances in a special, more accurate way.