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 VisiCalcspreadsheet on the Apple II platform. The machine was purchased in the thousands by finance workers (in particular, bond traders).
The next example is another spreadsheet, Lotus 1-2-3. Sales of IBM's PC had been slow until 1-2-3 was released, but only months later it was the best selling computer.
There have been a number of new uses of the term. For instance the Mosaic web browser is generally credited with starting the rush of computer users to join the Internet by showing them the World Wide Web. (Others argue that e-mail was the reason, though e-mail preceded the Internet.)