Refers to the most important or central part of something, often used figuratively for organizations, systems, or machines. Literally, it can mean the heart region.
This factory is the heart of the company.
The CPU is the core of a computer.
核心 means 'kernel' or 'core' of an issue or matter, often abstract. 心臓部 can be used for both concrete and abstract central parts, but carries a stronger nuance of being essential for functioning.
Compound of 心臓 (heart) and 部 (part, section). The figurative use follows the same metaphor as English 'heart' for the central or most important part.