The fictional metal used to make Bilbo’s and Frodo’s mail shirt is mithril.
Mithril is a rare, lightweight, and exceptionally strong metal found chiefly in Khazad-dûm, the Dwarven realm beneath the Misty Mountains. Its name comes from Sindarin and is commonly translated as “grey glitter.” Dwarves prized it, and the metal became more valuable than gold as its scarcity increased.
Bilbo receives a mithril coat from Thorin Oakenshield in The Hobbit. After Bilbo’s retirement, the shirt passes to Frodo, who wears it during the quest. It protects him from a spear thrust inside Moria and helps save his life during the Battle of the Pelennor Fields.
Mithril is not the name of Frodo’s sword: that weapon is Sting. It is also different from the Silmarils, which are legendary jewels created by Fëanor in the First Age.