Berkeley Systems released the famous "Flying Toasters" screen saver in 1989. It was part of the After Dark package for Apple's Macintosh computers.
It was stunning. Companies lost lots of productivity to employees staring at their screen savers. Screen savers brought a lighthearted element to the cold world of electronics.
Later, businesses realized that screen savers were a great place to leave branding. Company logos floating around screens became common. Also, marketing and sales information appeared scrolling across the screens of unused computers in retail outlets.
Eventually someone realized that with the power of the Internet, screen savers could extend the number-crunching capabilities of financially limited research institutions. Projects such as SETI@home and Climateprediction.net turn hordes of unused computers into massive distributed supercomputers with screen saver applications. IBM's involvement in the World Community Grid uses a similar approach for medical research, creating a grid with more power than many supercomputers.
When a computer is not in use, the screen saver activates. In most cases, your computer is not using its CPU to crunch numbers when in screen saver mode. In even a small organization, that is lots of idle time wasted, unless, of course, ...