The Silmarils (Quenya Silmarilli) were three gems of immense might and beauty created by Fëanor while the Eldar were still in Valinor. They were crafted of a substance unknown, and contained some of the light from the Two Trees of Valinor. After Fëanor was exiled to Formenos, the Silmarils were encased in a crystal casket.
Then Melkor, soon to be named Morgoth, killed Fëanor's father Finwë, the High King of the Noldor, and stole the Silmarils. Together with Ungoliant, he then destroyed the Two Trees and fled to the northlands of Middle-earth, where his ancient fortresses were. The Silmarils now contained all the remaining light of the Two Trees, and Fëanor was in a rage to have them back.
Fëanor, furious at Melkor and at the Valar's perceived desire to take the gems for their own purposes, swearing that he and his sons would not rest until the Silmarils were recovered, led the Noldor to Middle-earth. His flight, which began the First Age of Middle-earth, led to no end of grief for the Elves and eventually for the Men of Middle-earth. Five battles were fought for the Silmarils, which Melkor, now called Morgoth, had in his crown.
One of the Silmarils was recovered by Beren through great peril and loss. This stone was later taken by Eärendil to the Valar in the West as a token of repentance. The Silmaril was set by the Valar as a star. The other two gems remained in Melkor's hands, and were taken from him only at the end of the War of Wrath. However, soon afterwards, they were stolen by Fëanor's two sons Maedhros and Maglor. The jewels burned their hands, in refusal of their rights of possession, as they had burned Morgoth's hands many years before. In agony, Maedhros threw himself and his Silmaril into a fiery pit, and Maglor threw his into the sea. Thus the Silmarils remained in all three elements of Arda -- in the sky, soil and water.
See also The Silmarillion, the book which tells the story of the Silmarilli.