Balin is the dwarf whose tomb the Fellowship discovers in Moria in The Fellowship of the Ring.
Balin had been a companion of Thorin Oakenshield in The Hobbit. After the events of that story, he led an expedition into Moria and attempted to re-establish a dwarf kingdom there. The Fellowship finds evidence of that settlement, but the colony has been destroyed.
The discovery changes the group’s understanding of Moria. The chamber contains Balin’s tomb and a record describing the attack, while the drums and surrounding remains reveal that hostile creatures still occupy the mines.
Balin is easy to confuse with Gimli, the dwarf who travels with the Fellowship. Gimli is Balin’s relative and reacts strongly to the tomb, but he is alive and present with the party when the discovery is made.