What is system programming for linux exactly?

Answer 1

The main difference between application programming and system programming is application programming is for giving services to user but system programming is for making a platform for and giving services to other softwares. One of the best example of system programs is Operating System.

For system programming you usually need good knowledge of hardware.

So you may want to write a driver, kernel module, etc

Answer 2

For example you want to compile linux kernel from scratch with embedding some of your codes into the kernel for a customized distro or you make a device and want to write a driver for that so when it's connected to a linux machine it's recognized and works with the help of your driver or a kernel module (system call) which other software can call.