One of the realisations I only really had in my early 30s is that whether or not it's raining is much more localised than I thought. It can be raining here, and not at the shops a suburb over.

The percentage chance of rain includes whether or not it might rain in your specific dot of a given forecast area, which might be a suburb or entire city, as spelt out in your quote "at any given point in the forecast area".

The first time I drove over the Nullarbor in Australia, which has an entirely flat and straight 100+ KM section of road, I got to see rain far in the distance and experience driving into it having been able to clearly see it's edge from far out. That was an experience I had never had in the costal city I live in (Perth). That also led into similar realisations as the above.

It sounds so simple in theory but was not obvious to me for a long time :)