Boinc is a platform for volunteer computing. Briefly, volunteer computer is a system where computer processor’s idle time (those periods where your computer is on, but not being used for anything) is turned into calculation time via a custom written software.
This idea got a lot of attention with the seti@home project, where the computers of volunteers were transformed into a sort of supercomputer to analyse radio telescope date.
The Boinc project provides a platform where different projects can be created and launched on the platform’s website. Once online, volunteers can decide to which project they want to spare their computer cycles and help crushing numbers. Currently (11/12/14) the platform has about 229,396 active volunteers on 751,864 computers. with a 24-hour average of 8.024 PetaFLOPS. (not bad!)
Projects come from universities as well as private sector and range from medicine and mathematics to games.