Breaking or Tameshiwari in Japanese, has a long history that predated its use on Okinawa.
Schools don’t use it, or do as their history dictates. It is also a popular demonstration that some do.
The first thing to recognize is to recognize the objects being used can be broken. For example only Superman can break a ¾ inch piece of plywood. The objects being broken (all sorts) have some fracture point. Done incorrectly the person can break themselves. That possibility alone makes one consider if one has been properly trained for the break chosen.
That aside, at times I have punched and kicked through a single board. Done a front kick through 3 boards and a back side kick through 2 boards, an broken a cindercap with my forhead. But you do pay a price for doing breaks.
This article from Mas Oyama’s ‘Essential Karate’ is a good overview of breaking It does not contain every sort of break but enough to understand what can be done.
I consider breaking inappropriate for young students, and have never included it as part of my classes. This is for understanding what breaking consists of,Tame
And Tatsuo Shimabuku had his own demonstration skills.