The following description is taken from the Wikipedia page on Scrum. More information can be found here: http://en.wikipedia.org/wiki/Scrum
Scrum is a lightweight agile method for software development. Scrum is named after the Scrum in rugby, which is a way to restart the game after an accidental infringement. This entry describes the software development part of Scrum. This means that subjects like Scrum project planning, time/costs/risk management will not be explained in this entry.
Scrum was first applied in 1993 at Easel Corporation by Jeff Sutherland, John Scumniotales and Jeff McKenna when building an object-oriented design and analysis (OOAD) tool incorporating Round-trip engineering. At that time they needed a development method that had rapid application development and where product requirements could easily be translated into working code. These principles later became some of the basics of Scrum.
Some companies that applied variants of the Scrum approach for their projects are Fuji-Xerox, Canon, Honda, NEC, Epson, Brother, 3M, Xerox and Hewlett-Packard. These projects were observed and the results were published by Takeuchi and Nonaka in the Harvard Business review as “The New New Product Development Game” (January-February 1986).