I first remember the principle of least action while learning about Feynman diagrams. There a particle’s actual path is determined by calculating the action along all paths. All path integrals contribute to the particle’s motion with the largest integrals dominating. This is related to non-locality and is quite an amazing concept. But what got me was that there was this overarching physics concept called Action, that I had not been exposed to and could be applied to pretty much everything. I cannot explain it as well as Sabine Hossenfelder, so I won’t. Her YouTube explanation is short but covers the basics well.
The Closest We Have to a Theory of Everything - YouTube
If you want a more traditional explanation, you can read The Feynman Lectures on Physics Vol. II Ch. 19: The Principle of Least Action (caltech.edu).
This is a short post, but I hope with the linked material that it is an informative one.
Her video is very useful in explaining it all. And thanks for the heads up on the CalTech site. I see they posted much Feynman stuff for free use.
https://youtu.be/A0da8TEeaeE