It was designed by the Master in the guise of British Minister for Communications "Harold Saxon". Publicly, it was initially conceived as a secure defence communications system for Britain's armed forces, before growing into a public-private partnership whereby the satellites would also carry the first 4G mobile network; a network which was advertised as offering a more reliable service and cheaper calls.
However, the Master had an ulterior motive for putting the satellites in orbit, that is for the purposes of mind control, which was composed of a weak signal of four drumbeats, in which were coded a message telling humans to trust Saxon and vote for him in the upcoming 2008 UK general election. Vivien Rook had figured this out, but was killed by the Toclafane. She had planned for this, however, having an email be sent to Torchwood containing all of her gathered knowledge on Archangel, enabling Jack Harkness, Martha Jones and the Tenth Doctor to learn of the Master's plan. (TV: The Sound of Drums)
In an alternative timeline, one which was erased a year after it diverged, the Network advanced to give humanity a global consciousness by using a low-level psychic field, and was utilised to make all fear the Master and so be subservient to him. However, this telepathic field also caused the Master's demise, as when all the slaves on Earth revolted against the Master shouting cries and thoughts of "Doctor!" due to the stories told to slaves by Martha Jones, the Tenth Doctor (who had been aged 900 years by the Master's laser screwdriver) was rejuvenated, became a temporary sort of god. The timeline was then erased when the Master was distracted by Jack Harkness's destruction of the paradox machine in the Doctor's TARDIS. (TV: Last of the Time Lords)
Behind the scenes
The Visual Dictionary
It was a worldwide, mobile phone network that, from its 15 satellites, broadcasted the rhythm which allowed the Master to hypnotise Earth's population, giving him control over the people.