Three major types of software programs exist for computers today. The vast majority of users are familiar with only two: the applications software they use every day, like a Web browser or movie player, and system software, which includes operating systems like Windows, Mac OS X and Linux. However, these categories of software would not exist without a third type of software: programming software.
Applications software is the software that you probably use the most on a daily basis. Any program you use on your computer to get something done is an "application," although Windows also generally calls this kind of software "Programs." Application software comes in many types, including productivity software like OpenOffice, games like World of Warcraft or Web browsers like Firefox. On a Mac, you can open application software from the Dock or under Applications in the Finder. In Windows, shortcuts to many Applications are likely sprawled across your desktop, and you can access even more from the Start Menu under "All Programs."
System software is the software that runs your computer in such a way that you can actually interact with it, open applications, save files and be productive. The operating system, whether Windows, Mac or Linux, is a type of system software that starts your computer in a certain way, loads various programs when you log in, displays your desktop and files and communicates with your peripheral devices like printers and cameras. Most users should have limited interaction with system software, as tampering with it can be harmful to the computer. On Windows, these files are located in the WINNT (XP) or Windows (Vista) folder of your C:\ drive, whereas on Mac OS X these files are in every directory other than Applications and Users.
Programming software consists of the tools computer programmers use to create applications and system software. Chances are that your computer lacks programming software and that you have no need for it at all. However, if you want to build your own programs, then you will want this kind of software. Programming software also includes debugging and performance analysis programs.