It's been a few years since I've read the book, but if I recall correctly, what he's referring to as system code would be operating system code. System code would be the low level code that your application calls to allocate and free system resources like memory, UI windows, etc. or that sends a packet over the network. There's also the code that communicates with various pieces of hardware, such as graphics cards, hard drives, network cards, USB devices, etc. These are called drivers and are often considered system software as well.
Application software is generally the software that makes the applications you use on a computer or other device. This could be things like Microsoft Word or a game like Call of Duty or a tool like Photoshop. It could also be command-line tools like grep, awk, and find on Unix, or cd and dir on DOS. When you click an icon on the home screen of your phone or tablet, you're launching application code. Unless you work for an operating system vendor like Apple or Microsoft, or are working on the Linux OS, or writing the drivers for a hardware company, you are probably writing application code.