"Celegorm" was the Sindarin rendering of his Quenya mother name, "Tyelcormo", or "Hasty-riser" to describe his quick temper. His father name in Quenya was "Turcafinwë", or "Strong Finwë", meaning "strong-willed". ("Finwë" was a common family name among his House, it being the name of his grandfather Finwë, patriarch of the House and the High King of the Ñoldor.)
Celegorm was a great huntsman, and was a friend of the Vala Oromë. From Oromë he learned great skill of birds and beasts, and could understand a number of their languages. He had brought with him from Valinor the great hound Huan, a gift from Oromë.
As with the other Sons of Fëanor, Celegorm was bound by an oath to recover his father's Silmarils, which had been stolen by the Dark Lord Morgoth. His oath took him and his brothers to Middle-earth during the First Age where they established realms in exile, waged war against the armies of Morgoth, fought their own Elvish kind, and eventually brought ruin upon themselves.
While he and his brother Curufin lived in Nargothrond they captured Lúthien Tinúviel, daughter of King Thingol of Doriath. Celegorm wished to marry her, thus forcing a bond of kinship with Thingol. Huan, however, broke with his master and helped Lúthien escape.
Celegorm fell in the Second Kinslaying, when the Sons of Fëanor attacked Doriath to seize a Silmaril in the possession of the Elvish King Dior the Beautiful of Doriath. Dior and Celegorm slew each other in the halls of Menegroth.