A killer application (commonly shortened to killer app) is a computer program that is so useful that people will buy a particular brand of computer simply to run that program.
The first example of a killer app is generally agreed to be the VisiCalc spreadsheet on the Apple II platform. The machine was purchased in the thousands by finance workers (in particular, bond traders).
Today there are a limited number of platforms in the world, and the vast majority of the world runs on the Windows platform. It is unlikely that there will ever be another killer app that will cause people to purchase an entirely new machine.
There have been a number of new uses of the term however. For instance Mosaic is generally credited with causing the majority of computer users to join the internet, while others argue that e-mail was the reason.