The Great Intelligence was a formless entity, wandering in space. It first encountered the Eleventh Doctor in 1892, when it took the form of snow. It found an ally in Doctor Simeon, and through him attempted to create a race of ice-people.
In 1935, the Second Doctor encountered the Intelligence living in the mind of Buddhist monk Padmasambhava, keeping his frail form alive for hundreds of years. It was through him that the Intelligence tried to manifest itself in physical form as robot Yetis. It returned once more as a mysterious London fog that consumed everything it touched in a web-like substance. This attempt at corporeal form was thwarted, when the Intelligence’s control spheres were destroyed. But the Great Intelligence escaped once more.
Moving ahead to 2013, The Great Intelligence used the wi-fi to capture and imprison humans - only to be thwarted by The Doctor and Clara. Shortly after, and still using the form of Doctor Simeon, the entity would come face-to-face with the Doctor on Trenzalore where it planned to enter the the Gallifreyan's time stream and rewrite his history and, in the process, sacrifice itself. Luckily, for the Doctor, Clara was on hand to help out and save him from The Great Intelligence's machinations.