"Greensight" is the magical ability to perceive future, past, or contemporary but distant events in dreams. It was one of the talents of the Greenseers of the Children of the Forest. Some humans are also born with this ability.
Bran Stark experienced a prophetic dream that his father was in the crypts of Winterfell when Eddard Stark was indeed executed in King's Landing. His younger brother Rickon also experienced a similar dream. Jojen Reed later explains to Bran that this was greensight, and that he had a similar dream the day Eddard was killed. When he told his father Howland Reed about the dream he openly wept, realizing that it meant that his great friend Eddard had died.
- Greensight at A Wiki of Ice and Fire (MAJOR spoilers from the books)