Wikipedia defines a "Kernel" as:
which I don't think is a very good definition. A kernel in my mind is something which manages the computers resources (memory, disk, processor time etc) and abstracts the hardware.
The marketing division of the Sirius Cybernetics Corporation defines a Kernel as
Your plastic pal that's fun to be with.
The Kernel internals is mostly hidden from users; originally, the kernel was surrounded by a Shell and user applications use the shell. (Think of a nut or stone-fruit - a kernel encompassed by a shell).
The kernel can have bits loaded at run time; each bit is called a Kernel Module.
Linux is an example of a MonolithicKernel, while TheHurd is an example of a MicroKernel
Remember, you can't boot a kernel by itself, hence the ReligiousWar of RMS vs common usage. Attempting to boot "Linux" would result in something along the lines of "Kernel Panic: Cannot find init". Trying to boot what RMS calls GNU/Linux would result in the OS we know and love.
97 pages link to Kernel: