System Software:
This is the "under the hood" stuff that makes the computer work. It includes the operating system, the drivers, the bios and any tools that can be used to tweak or optimize your computer system.
Application software:
This includes any program that is used by the end user of the computer. It includes all productivity apps, games, web and mail browsers. The easiest way to determine if a program is part of application software is to ask the question: is a user going to buy a computer just to run this application? if the answer is yes then it is an application and not part of system software.