The Great Weapons are the greatest magical weapons ever forged by mortal hands. The mortal weapons crafted by the Elves and the Dwarfs are surpassed only by artifacts such as the Sword of Khaine and the Axes of Grimnir (Posessed by the Dwarfs; High King Thorgrim Grudgebearer and Gotrek Gurnisson, a Slayer) that were forged by the very Gods of the Warhammer World themselves.
The Great Weapons of Ulthuan are relics of the Great Chaos Invasion. They were forged at the shrine of Vaul's Anvil (to the smith-god Vaul), using Vaul's Hammer, by the great Archmage Caledor Dragontamer and Aenarion the Defender, the first Phoenix King. At the time, the Great Weapons were given to the mightiest warriors who had rallied to Aenarion's banner, meant to give them a fighting chance against the Daemonic hordes of Chaos.
After the Invasion ended, however, the Great Weapons took on an additional meaning. When Aenarion died after the Second Invasion, there was no precedent as to how the next Phoenix King had been chosen. Aenarion had been acclaimed by the people as their Phoenix King, but given that Aenarion had been chosen by the god Asuryan, there wasn't a formal process. Eventually it was decided that the owners of the Great Weapons, who had been Aenarion's closet advisors and the most powerful and respected Elves in the land, should decide whether to anoint Aenarion's son, Malekith, or to chose another candidate. Unfortunately for Malekith, they chose Bel Shannar, an Elf from Tiranoc who was one of their number, and Malekith's ire at this later provoked him to start the Elven Civil War known as the Sundering.