if your phone's a car, think of the kernel as the driver. it controls the power sent to different aspects of the phone which will then affect performance, battery life & overall feeling of the phone. it'll also allow you to overclock/underclock your device.
kernels can be customized by the developer to only allow certain processes to consume X amt of battery--thereby extending your battery life at the expense of screen brightness or refresh. it can also be used to control extraneous processes from running.
as with any mod--be careful which kernel you apply. it can seriously damage the hardware if the kernel isn't made to interact with your device.
if some bit of hardware requires constant X power/processing consumption but the kernel only allows 1/2X power/processing consumption, then it's gonna put a strain on multiple components and ultimately dmage your phone to the point of you cursing the Androidgods.
i've left out a bunch--this explanation is just something easy to remember.
different kernels allow/won't allow certain applications to run--or will not interact nicely with them (wireless tether on some kernels), so be careful which one you choose to apply.