You may already know that the verb savoir means “to know.” But did you know that, when followed by an infinitive, it can also mean “to be able to” or “to manage to" (synonymous with pouvoir)?
The Paris-Meudon Observatory...
a su garder sa spécificité d'astrophysique
was able to keep its astrophysical specificity
Captions 18-20, Voyage en France - MeudonPlay Caption
L’article a su le convaincre à recycler.
The article managed to convince him to recycle.
It’s easy to see that “know” wouldn’t really work in either of these examples, since their subjects aren’t human. You wouldn’t say that the Paris-Meudon Observatory “knew” how to keep its astrophysical specificity, nor that an article “knew” how to convince someone.
On the other hand, there are plenty of cases where savoir plus an infinitive can go either way:
Pour quelqu'un qui sait faire la cuisine.
For someone who knows how to cook.Play Caption
Bref, Jean de La Fontaine fait partie pour moi de ces auteurs intemporels
In a word, Jean de La Fontaine is for me one of those timeless authors
qui à travers une forme littéraire intéressante
who, through an interesting literary form,
a su toucher le fond de la nature humaine.
was able to reach the depth of human nature.
Captions 38-40, Le saviez-vous? - Jean de La FontainePlay Caption
We could just as well switch the translations here: “someone who can cook”; “Jean de La Fontaine… knew how to reach the depth of human nature.” "To be able to" and "to know how to" are more or less synonymous, so it makes sense that they overlap in the same French verb.
Just note that the other verb for "to know," connaître, doesn't have this extra connotation. While savoir means "to know how to" or "to be aware of," connaître means "to know someone" or "to be acquainted/familiar with."