What are the differences between kernels?
 

As a total newbie, I have to ask this most fundamental question? What is the purpose of upgrading your kernel? In the Windoze world, is it analagous to XP updates, where security holes and the like are being patched? Thanks in advance.

Depending on what distro you are using you might not have to upgrade your kernel. Kernel upgrades fix any bugs that are found, and also add new features and support for hardware. Securiy holes, like this one are also fixed.

I understand the bugs, but what kind of new features? I'm trying to understand exactly what happens at the kernel level.

On a slight tangent, is it safe to say that, with each upgrade, the kernel keeps getting bigger and bigger?

try reading the kernel Changelogs

http://www.kernel.org/pub/linux/kernel/v2.6/

its not necessary analogous to Windows update, since the kernel itself doesnt make up the whole operating system.
Update services that distro vendors provide(Redhat's up2date, Suse's online update etc) are more like it.

Not significantly unless you add more features and support. Try downloading some kernel sources, unpack them, and then go into that dir and type 'make menuconfig' or see if there is anything in /usr/src/linux