Define and shortly explain the difference between system software and application software?

At a very high level: Systems Software is "Middleware" that runs the infrastructure that supports the application software. Most people never notice or interact with this software unless it breaks and then you get frustrated because you can't do your normal job or transaction. Application Software is the software that most end-users are familiar with and where the "work" is done by the average person, i.e. order entry, billing, data searching, etc.