From Knoppix Documentation Wiki
The kernel is the core of the operating system. It's primary functions are controlling execution of processes, handling memory management, providing a filesystem, and providing a portable interface through which programs may communicate with hardware.
A kernel image is a compiled and usually compressed & self-extracting kernel (generally with the name of bzImage). In the linux distributions, it is copied from /usr/src/linux/arch/i386/boot/ to /boot .
The uncompiled kernel source can be obtained from  in .tar.gz or tar.bze format . To compile the system one uses "make xconfig" in XWindows environment and later make dep; make clean; make bzImage; to compile the modules make modules make modules_install.
The kernel image is booted changing [Lilo] /etc/lilo.conf :
See also kernel panic