Just trying to get a firm grasp of key concepts before attempting a kernel compile...

What are 'system header files'? Can't find a decent answer to this question.

According to the Linux Wiki, you need them installed along with the C compiler and make, whatever they are.

If you've installed the kernel sources, you do have the system header files. The 'C standard library headers' are the headers containing functions provided by the standard c library (libc/glibc).

Thanks for that Matir. Still not sure exactly what a header is, but it seems it doesn't matter so that's alright.

header files "*.h" files in c and c++ define the functions available for use by client programs.
they expose the interface to the user space library i guess you would say

now when you say system header files and talk about the kernel i assume you mean the kernel interface available through glibc.

these files are in /usr/include/linux and /usr/include/asm and are specific to glibc -- they are kernel header files from a kernel source package but specifically the ones used to compile glibc so they expose the kernel interface compiled into glibc that other user space programs can use. These files always stay the same and don't change when you change the kernel.

beyond that there are other header files that expose what would be called "system" as well to user space and come with glibc. These non standard c language functions also represent kernel interface and why some come in the kernel source and some come in glibc source is a mystery. glibc and the kernel form a kind of which came first the chicken or the egg kind of thing.
anytime the programmer is using functions that are from a lower level than the standard c or c++ functions they are using "system" functions.

the important thing to get is these files in /usr/include are different from your kernel source directory.
The kernel source directory contains the headers that describe kernel space as opposed to user space.
when you compile or write something that is actually a part of the kernel like a kernel module you use the kernel space headers and you have access to the inner nuts and bolts of the kernel and don't have to access the kernel through glibc.

Thanks for that, foo_bar_foo!

The whole thing makes a bit more sense now.