Foretelling is the ability to tell the future with unerring accuracy, if not always great clarity. The ability is believed to be linked to the One Power by Aes Sedai, and is thus classified as a Talent even though it requires no active use of the Power. Indeed, it is usually not under the control of the speaker as to when it comes upon her (or him), and sometimes they do not remember, themselves, what they have Foretold.
"He is born again! I feel him! The Dragon takes his first breath on the slope of Dragonmount! He is coming! He is coming! Light help us! Light help the world! He lies in the snow and cries like the thunder! He burns like the sun!"
"From this day Andor marches toward pain and division. The Shadow has yet to darken to its blackest, and I cannot see if the Light will come after. Where the world has wept one tear, it will weep thousands. This I Foretell. This, too, I Foretell. Pain and division come to the whole world, and this man [Rand] stands at the heart of it."
—Elaida do Avriny a'Roihan
When Rand asks Amys about his mother after he returned from Rhuidean, Amys tells him the story of Shaiel and one part is a Foretelling of Gitara Moroso.
"An Aes Sedai called Gitara Moroso, who had the Foretelling, had told her that disaster would befall her land and her people, perhaps the world, unless she went to dwell among the Maidens of the Spear, telling no one of her going. She must become a Maiden, and she could not return to her own land until the Maidens had gone to Tar Valon.""
"The lion sword, the dedicated spear, she who sees beyond. Three on the boat, and he who is dead yet lives. The great battle done, but the world not done with battle. The land divided by the return, and the guardians balance the servants. The future teeters on the edge of a blade."
"The White Tower will be whole again, except for remnants cast out and scorned, whole and stronger than ever. Rand al'Thor will face the Amyrlin Seat and know her anger. The Black Tower will be rent in blood and fire, and sisters will walk its grounds. This I Foretell."
"I see him before you! Him, the one who lives many lives, the one who gives deaths, the one who raises mountains. He will break what he must break, but first he stands here, before our king. You will bloody him! Measure his restraint. He speaks! How was the fallen slain? Tellindal Tirraso, murdered by his hand, the darkness that came the day after the light. You must ask, and you must know your fate. If he cannot answer, then you will be lost. You will bring his end swiftly, so that the final days may have their storm. So that Light may not be consumed by he who was to have preserved it. I see him. And I weep."
—Recited by King Paitar of Arafel
The prophecy was given to Reo Myershi, the ancestor of King Paitar, and was held in secret by his line until Paitar told it to other Borderlands rulers. They decided to test Rand and try to kill him if they must. The meeting took place in the Far Madding Guardian. First all four rulers struck Rand, bloodying him, then Paitar asked Rand about the death of Tellindal Tirraso, being ready to kill him right there. When Rand answered properly, they relaxed.
If Rand didn't have Lews Therin's memories, he wouldn't be able to answer the question. And before his epiphany, according to Rand himself, he would "return those slaps with balefire", because the Guardian cannot block the True Power. The Borderlander armies had orders to attack in that case.