An application is a software program that provides some kind of interactive service to the person running it. They provide an interface for the user to use to interact with the program.
Examples of applications are:
- Word processor
- Email client
- Music streaming application
- Video playback application
- News feed reader
What is not an application is a software program that runs in the background - for example a print spooler. This type of program tends to be called a 'background process'.
With smart phones the word has been abbreviated to just 'Apps'.
Deciding on an application usually involves the question "I need to do XYZ on the computer (or phone)". Then the job is to find an application that can do it.