Kernel:

Kernels are the core components of operating systems. They are the central portion that manages memory, files, peripherals, and system resources. The kernel typically runs processes and provides interprocess communication among those processes. Common core functions include scheduling and synchronization of events, communication among processes (message passing), memory management, management of processes, and management of input and output routines.

- the Linktionary

Kernel:

The essential part of Unix or other operating systems, responsible for resource allocation, low-level hardware interfaces, security etc.

- the Free On-line Dictionary of Computing

Kernel:

Modern operating systems are typically built in layers, with each layer adding new capabilities, such as disk access techniques or a graphical user interface. But the essential layer, the foundation on which the rest of the operating system rests, is typically called a kernel. In general, the kernel provides low-level services, such as memory management, basic hardware interaction, and security. Without the kernel, your system would stop.

- the CNET Internet Glossary