From the FreeOnLineDictionaryOfComputing:

	1. <operating system> The essential part of Unix or other operating systems, responsible for resource allocation, low-level hardware interfaces, security etc. See also MicroKernel. 

	2. <language> An essential subset of a programming language, in terms of which other constructs are (or could be) defined. Also known as a core language.

The first sense is the most common.

Another sense is related to ImageProcessing: a kernel is a small matrix used in convolution and various other operations.

The term is also sometimes used in reference to the "core" of some application.

----
CategoryOperatingSystem CategoryDefinition