The purpose of an operating system’s kernel is to manage the system's resources and facilitate communication between hardware and software. It acts as a bridge, enabling applications to interact with hardware components like CPUs, memory, and storage. The kernel handles tasks such as process management, memory management, and input/output operations, ensuring efficient allocation and smooth performance. It operates in a privileged mode, allowing it full access to hardware resources, while applications run in user mode with restricted access for safety and stability.