They are twin brothers, the youngest of the thirteen Dwarves who set out on Thorin Oakenshield's quest along with Gandalf and Bilbo Baggins. They are Thorin's nephews, and are identified by their blue cloaks and yellow beards. Fíli and Kíli can only be told apart because Fíli has a longer nose.
Both brothers are killed in The Battle of Five Armies, as well as Thorin himself, and all are buried with honour.
Tolkien borrowed the names of Fíli and Kíli from characters in the Edda by Snorri Sturluson.