The Lost Light: A Brief History:

Before Man, before Hobbits, before Dwarfs, and even Elves, the Valar gods created two sources of light to give life to Arda.  When these lamps were destroyed by the Dark Lord Melkor, their essence was formed again into Two Trees that continued to give light to the earth.  Melkor poisoned the trees, stealing the Silmarils, three gems crafted by the Elves from the tree sap containing their light.  From the last flower and fruit of the dying trees, the Valar created the moon and the sun to give light again to Arda, and various relics were created containing tiny measures of the lost light that once shone in the Two Trees.  As for the Silmarils, one of the gems was recovered in the wars of the First Age and set as a star in the sky; the other two were lost forever.

The Fountain of Galadriel, from which the Phial was filled and given to Frodo Baggins as a light to use in dark places, was one such relic containing small amounts of the lost light from the recovered Silmaril.  The Star of Elendil, a relic inherited from Elendil by Isildur, King of the Dúnedain, also contained trace amounts of the light of the Two Trees.  This jewel was lost with him in the Great River when he was waylaid by Orcs.  A second Star, known as the Star of the Dúnedain, was made for his descendants which became the symbol of the North-kingdom and remained in the hands of Isildur's heirs until the time of Aragorn.  The original Star, lost for over 3000 years, was rediscovered by the Guardians of the Lost Light amongst Saruman’s treasures in a secret chamber of the Tower of Orthanc.  It was returned to its rightful heir, Aragorn, Chieftain of the Dúnedain, King of Gondor. 

Sources:  Wikipedia, "Two Trees of Valinor." | Wikipedia, "Quenta Silmarillion." | Wikipedia, "Silmaril." | The Encyclopedia of Arda, "Star of Elendil".