The kernel is the central software component of all Linux systems. Its capabilities very much dictate the capabilities of the entire system. If the kernel you use fails to support one of your target's hardware components, for instance, this component will be useless as long as this specific kernel runs on your target.
Many books and online documentation already discuss the kernel's internals, its programming, its setup, and its use in user systems at length. I will not, therefore, cover these issues here. If you are interested in such issues, have a look at Running Linux, Linux Device Drivers, and Understanding the Linux Kernel by O'Reilly. These books cover the kernel's setup and use, its programming, and its internals, respectively. You may also want to take a look at the Linux Kernel HOWTO available from the LDP.
Our discussion will be limited to issues about the preparation of a Linux kernel for use in an embedded system. Specifically, we will discuss kernel selection, configuration, compilation, and installation. Each step will get us closer to the goal of obtaining a functional kernel with its related modules for our target system. Our discussion will end with coverage of the aspects of the kernel's operation that are specific to embedded systems.