The Silmarils were three gems made by Fëanor from an unknown material, which he filled with living light from Laurelin and Telperion, the Two Trees of Valinor. These became his pride and joy, as they were his greatest works. However, they were coveted by Morgoth, who stole them when he decided to escape from Valinor. This caused Fëanor to rage in fury, almost to the point of insanity. This precipitated a huge string of tragedies that included the Kinslayings and the Sinking of Beleriand (the latter somewhat indirectly).
One Silmaril was stolen back from Morgoth by Beren and Lúthien Tinúviel, and was eventually given to the Valar by Eärendil as a token of repentance on the part of the Noldor as a whole. This Silmaril was set in the sky as a star. The other two eventually came into the hands of Maedhros and Maglor, two of Fëanor's sons, and at the end of the day wound up in a fiery pit and at the bottom of the sea respectively. Thus all three elements of Arda (sky, fire, and water) were represented, as Elrond will be certain to point out in his Numerology 101 class.
There were always three Silmarils, and the presence of any more is a definite sign of worry for a PPC Agent on the job. Silmarils, of course, are high on the list of items that are Absolutely Forbidden to be taken into possession of PPC Agents -- a recent development that was enacted only after a bitter fight over ownership of one sent three Agents to Medical[source, please!].