Children of the Forest
The Children of the Forest, sometimes referred to simply as the "children" are a mysterious non-human race that originally inhabited Westeros continent, long before the arrival of the First Men during the Dawn Age, more than 12,000 years ago. The giants call them woh dak nag gram ('little squirrel people'). They call themselves in the True Tongue those who sing the song of the earth. 
Little is known about the children. They are a mysterious and magical people who have not been seen by humans for thousands of years. Tales describe them as diminutive humanoid creatures, dark and beautiful, at their tallest no larger than an human child. They are long-lived. Their true names would be too long for human tongues.
The children did not use metal, weave cloth or build cities; instead they lived off the land, using stone implements, wearing bark leg-bindings and shirts of woven leaves, dwelling in caves, crannogs, and hidden tree villages. Males and females both hunted side by side. The children had no books, no ink, no parchment and no written language.  They were a people with a deep connection to the land.  The children wielded obsidian weapons and bows in battle, but also used powerful magic.
Legends say the children of the forest were gifted with supernatural powers and magic; having power over the beasts of the wood, the ability to wear an animal’s skin, and the skill to create music so beautiful as to bring tears to the eyes of any who heard it, and the greensight ability (although the Maesters believe that the greensight was not magic, simply another kind of knowledge). It was the children who carved the faces on the weirwoods to keep watch over the woods. They believe that their wisdom had something to do with the faces in the trees  The children of the forest believed that the weirwood trees were the Gods, and when they died they became a part of them.
They were smaller than men with nut-brown skin, dappled like a deer's with paler spots. They had large ears that could hear things that no man could hear.
They usually had large eyes, great golden cat's eyes, that could see down passages where a boy's eyes saw only blackness. They have vertical, slit-like pupils; this trait is responsible for improved night vision and typically associated with a nocturnal lifestyle in such creatures as cats (the Children's eyes are described in A Dance With Dragons as resembling cats' eyes) and many species of snakes, including nearly all vipers (despite Doran Martell's reference to his brother Oberyn's "viper eyes," however, the Red Viper is never described as sharing this feature with the Children of the Forest). A few had green or red eyes; these had the gift of greensight and were known as greenseers.
Their hands had only three fingers and a thumb, with sharp black claws instead of nails. The children were slight, quick, and graceful.
“They were a people of the Dawn Age, the very first, before kings and kingdoms, in those days, there were no castles or holdfasts, no cites not so much as a market town to be found between here and the sea of Dorne. There were no men at all. Only the children of the forest dwelt in the lands we now call the Seven Kingdoms.” 
It is unknown for how long the children lived alone in their land, nor where they themselves came from, but for thousands of years they had, what later becomes known as "Westeros", to themselves. Eventually about 12,000 years ago, the children came in contact with the First Men, the first outsiders. These invaders brought with them bronze, great leathern shields, and the first horses and their own gods. Burning the great Weirwoods as they came, leading to war between the two.
For roughly 2,000 years two races fought a desperate war for dominance. The children used their magic to shatter the Arm of Dorne, the land-bridge through which the First Men came, in a futile attempt to end the invasion and later flooded the Neck - where legend has it that the children called upon their gods from the Children's Tower to send the hammer of the waters to smash the Neck, as they smashed the Arm of Dorne, but it was not enough to stop the advance of the First Men. The histories say that some of the First Men, the crannogmen, grew close to the children of the forest in the days when the greenseers tried to bring the hammer of the waters down upon the Neck. 
Eventually the First Men and the children fought one another to a standstill. The two races agreed to peaceful coexistence and signed the Pact on the Isle of Faces, granting the open lands to humanity and the forests to the children.
The Pact lasted for 4,000 years before the enigmatic Others invaded from the uttermost north, bringing death and destruction to both races, during an extended period of winter known as The Long Night, the children of the forest joined with the First Men, to fight against the Others in the War for the Dawn. Eventually the Others were driven back into the Lands of Always Winter.
After the War for the Dawn, the First Men and the children of the forest lived in relative peace, but in these years, the children of the forest began their slow withdrawal from the lands of men, retreating deeper into their forests and beyond the Wall. During the Age of Heroes it was also recorded by the Night's Watch that the children of the forest gave the black brothers a hundred obsidian daggers every year.
The children of the forest taught the worship of the Old Gods to the First Men, but the Old Gods were largely supplanted in the South by the Faith of the Seven after the Andal Invasion. A hill, now known to the Westerosi as High Heart, was sacred to the children of the forest. There the Andal king named Erreg the Kinslayer cut down the children’s grove of thirty-one weirwoods.  High Heart is said to be haunted by the ghosts of the children who died there, likely defending their grove from Erreg. Some of the children’s magic is said to still linger at High Heart.
Although people in Westeros believe the children of the forest to be extinct there are a few that still live in the world of men. A dwindling remnant of their population is located far north of the Wall, in a cave system under a hill; the entrance is a warded cleft in the hillside.
The caves are timeless, vast, silent. They are home to more than three score living singers and the bones of thousands dead, and extend far below the hollow hill. The children of the forest live with whom they refer to as the Last Greenseer. In the caves there are passages that go deep, bottomless pits and sudden shafts, forgotten ways that lead to the very center of the earth. Leaf tells Bran Stark that even the children of the forest have not explored them all, even though they have lived there for a thousand thousand man-years. Bran realises that they are indeed singers, he hears them singing. They sing sad songs in the True Tongue so he cannot understand the words, but their voices are as pure as the winter air. 
Gone down into the earth … Into the stones, into the trees. Before the First Men came all this land that you call Westeros was home to us, yet even in those days we were few. The gods gave us long lives but not great numbers, lest we overrun the world as deer will overrun a wood where there are no wolves to hunt them. That was in the dawn of days, when our sun was rising. Now it sinks, and this is our long dwindling. The giants are almost gone as well, they who were our bane and our brothers. The great lions of the western hills have been slain, the unicorns are all but gone, the mammoths down to a few hundered. The direwolves will outlast us all, but their time will come as well. In the world that men have made, there is no room for them, or us.
To Bran Leaf seemed sad as she told him, and that makes Bran sad as well.
It is only later that he reflects and thinks to himself, Men would not be sad. Men would be wroth. Men would hate and swear a bloody vengeance. The singers sings sad songs, where men would fight and kill.
Known children of the forest
“The children . . . live only in dreams. Now. Dead and gone.” 
– Maester Luwin
“All that is left of them are the faces on the trees."
– Maester Luwin
“The children are gone from this world, and their wisdom with them. 
– Maester Luwin
“The children of the forest could tell you a thing or two about dreaming.” 
“Leaf and her people were far from childlike. Little wise men of the forest would have been closer. 
References and Notes
- A Dance with Dragons, Chapter 13, Bran II.
- A Dance with Dragons, Chapter 34, Bran III.
- A Game of Thrones, Chapter 66, Bran VII.
- A Clash of Kings, Chapter 28, Bran IV.
- A Clash of Kings, Chapter 50, Theon IV, p 733.
- A Feast for Crows, Chapter 5, Samwell I.
- A Storm of Swords, Chapter 22, Arya IV, p 249.
- A Game of Thrones, Chapter 66, Bran VII, p 736.