Greensight is the ability to have prophetic dreams called "Green Dream". A person with greensight sometimes dreams as other people, but the "Green Dream" are different, filled with symbolic meaning, images, and metaphors of what is to come. The meaning behind the dreams is not always obvious, but once you have experienced one, you will see the fulfillment of your visions in the unfolding of the events around you.
Some of the children of the forest reputedly had greensight. Their wise men were called Greenseers. Crannogmen who keep many of the old ways, were also known to have greensight, one of them is Jojen Reed, who has unnaturally green eyes. It is possible that this is the result of his advanced greensight abilities.
Supposedly these dreams can concern the dreamer or another person, but the dreamer will be able to tell the difference. Greenseers might also dream of his/her own death.
Wargs have been known to also possess this ability.