Down the road from my house, each apple in the Harner Farm orchard has a core. The Breazeale Nuclear Reactor on Penn State’s campus has a core where fission occurs. Many colleges have a core curriculum program. Most skyscrapers in Manhattan have a vertical core for elevators, stairways and utility lines and wires.
A core is a central and foundational part of something. Without it the rest of the something will often not function.
However, here in America in the 21st century the word core is more and more often being used to describe a part of ourselves. Our cores. And more specifically, how to train and improve our cores. Talk to anyone who is getting or staying physically fit these days and they will tell you about how they are strengthening their core muscles.