The operating system is used to manage system resources and give application software an environment in which it can run. It acts as an intermediary between the user, the software and the computer hardware. When the computer is turned on, the primary parts of the operating system are loaded into memory and stay there while the PC is turned on. While booting up, it configures the hardware and makes sure everything is connected and then runs many software tasks in order to get the operating system working in a way that a user can interact with it.
Application software is the front-end software that users handle. Common applications, such as Microsoft Office, Google Chrome and Skype are generally installed by the user and are required to undertake particular tasks. Application software, such as antivirus programs, will usually start when the PC is turned on and run in the background after the operating system has loaded all of the necessary services and programs.
Quick Answer:
System software is also known as the operating system and includes Microsoft Windows, Apple's OSX and Linux, while application software refers to programs that perform tasks and includes Microsoft Office, Adobe Photoshop and Apple iTunes. Application software requires an operating system to be installed and booted up before it can be used.