"I crafted these," he whispered. "I made them to never break. But I knew, as I did it, that they would eventually fail. Everything eventually fails when he touches it.."
– Rand to Egwene before the Last Battle
The Great Seals are seven cuendillar discs, each bearing the ancient symbol of the Aes Sedai (a white teardrop and a black teardrop conjoined). They are the size of a man's hand and serve as a focus point for the actual seals which hold the Dark One in his prison. 
When the forces of the Shadow were about to overrun the forces of Light and defeat seemed only months away, Lews Therin Telamon and the Hundred Companions decided to execute their dangerous plan to reseal the Bore that allowed the Dark One to touch the earth. They, together with a bodyguard of ten thousand warmen, Traveled to Shayol Ghul to execute their plan, sealing away the Dark One and the thirteen Forsaken. Strictly speaking, the discs themselves are not seals, but are as focus points, or anchors, for the seals. However, in common usage they are referred to as Seals.
Currently, even though the seals are made of cuendillar, the entropic influence of the Dark One has caused them to weaken to such an extent that they could shatter from a fall to the ground or being struck by a man with a hammer.
The Breaking and after
The histories are unclear about precisely when the seals were dispersed to hidden locations, but there is sufficient information to deduce that they were scattered either toward the end of the Breaking of the World , or shortly thereafter, to prevent a maddened Aes Sedai, or worse, a Shadowspawn from gaining possession of these focus points.
Only a few knew of their hiding places, including the Amyrlin Seat; indeed one of her titles descended from that time is "Watcher of the Seals." The knowledge of their secret locations, however, was lost during the Trolloc Wars. 
Upon delivering one seal to Rand al'Thor, Mazrim Taim tells the story of how he obtained it: a farmer—who claimed descent from royalty during the Trolloc Wars and then nobility during Artur Hawkwing's reign—had guarded the disc for two thousand years until Taim passed by. The man, old and without heirs, thought Taim was the Dragon Reborn, so he gave it to him for safekeeping.
Recently, the Seals have begun to resurface and are no longer invulnerable.
Status of the Seals
|Discovery||Status|| Location (intact)/|
|In the Eye of the World after drained by Rand al'Thor ||Broken||At discovery|
|Bought by Bayle Domon from a Saldaean antiques dealer, confiscated by the Seanchan High Lord Turak; later found by Moiraine Damodred||Broken||During the battle at Falme|
|In Turak's possession, possibly brought from Seanchan; later found by Moiraine|
|By Moiraine in the Great Holding in the Stone of Tear||Broken||By Logain Ablar during Tarmon Gai'don|
|By Moiraine in Rhuidean ||Broken|
|By Nynaeve al'Meara at the Panarch's Palace in Tanchico||Broken||During the journey from Samara to Salidar|
|Given to Rand al'Thor by Mazrim Taim, who says a Saldaean crofter gave it to him ||Broken||By Logain during Tarmon Gai'don|
Breaking the final Seals
Research by Min Farshaw, prompted by a cryptic note from Herid Fel, indicates that the Seals need to be destroyed before the Bore can be made whole or resealed properly. Rand announced his intention to do just that to the Amyrlin and the Hall of the Tower, announcing they would discuss it at a fixed date at the Field of Merrilor. The Aes Sedai are, for the most part, opposed to the idea, and Egwene al'Vere is gathering leaders to oppose him at that meeting. Gathering them appears to be exactly what he wants, though he intends to break them in any event.
Later during the negotiation about The Dragon's Peace at the Field of Merrilor, Rand surrenders the remaining three unbroken seals to Egwene, the Amyrlin Seat. She is at the same time told by Moiraine Damodred that Egwene herself will break them. Moiraine asks if Egwene has Dreamed of Rand breaking the seals to which she replies that she has Dreamed him walking on the shards of the broken seals indicating they have been broken already. Later Rand checks in on Egwene and asks to see the seals. While inspecting them he finds they are not the real things, as he had crafted them thousands of years ago as Lews Therin Telamon. The seals that Rand had been carrying around, had in fact been counterfeits.
From the conversation between the Forsaken and later between Rand and Egwene, it is found that the seals were stolen by the Dark One's minions and replaced with fakes. In fact the Dark One now holds keys to his prison. Mazrim Taim reveals that he is the one who has stolen them and now holds them on his person. Androl Genhald manages to steal them from Taim while under the Mask of Mirrors as Varil Nensen. He hands them over to Logain Ablar, who breaks them on seeing the lance of white light released when Rand forges the Dark One's new prison. Gabrelle names him sealbreaker.