Types of Software
There are two basic types of software : System Software, and Application Software
System Software is software that is designed to run and maintain a computer system. The most important piece fo system software is the Operating System , for example Windows, or Android (click here for details on what an OS does).
Another important group of system software is Utilities Software - these help maintain or configure a computer - for example Backup Software, Disk Checkers, Encyryption Software (click here for more on Utilities)
Application Software (apps) are the "programs". Common application software includes Word Processors (like Ms Word), graphics software (like Adobe Photoshop), email clients (like Ms Outlook), web browsers (like Google Chrome). The software skills section contains some guides on how to use certain application software we use in school.
Proprietary and Open Source
When writing software the developers have a choice they can make it Open Source which means that its code can be viewed and edited by users if they choose to, or they can make it Proprietary which means that the source code can not be seen, or edited by users. There are advantages and disadvantages to both approaches . More on this can be seen here (open) and here (proprietary).