For those who are not familair with the Silmarillion, here is a short explanation of the battles Erestor mentions:

Dagor Bragollach = the fourth battle of the Wars of Beleriand, known as the Battle of Sudden Flame.

Once Morgoth broke the Siege of Angband, which had held for four hundred years. On a winter's night, Morgoth sent out rivers of flame, consuming Ard-galen, which was renamed Anfauglith. Many elves perished as they fled from these flames, from the fire and the smoke. His armies of Balrogs and Orcs, led by Glaurung first of the dragons, overran the highlands of Dorthonion, and slew Angrod and Aegnor. Maglor's horsemen were burnt alive on the plain of Lothlann, and Maglor's Gap was taken, giving Morgoth an entry into Beleriand itself. Maglor retreated with heavy losses to Himring, where he helped defend the city of Maedhros.

Dagor-nuin-Giliath = also called the battle-under-stars. It was fought before the rising of the Moon between Fëanor and his people, who had just returned to Middle-Earth from Valinor, and Morgoth's forces. The Elves were victorious but Fëanor was slain by a Balrog and Maedhros captured.

Translations of names used:
Ferineth = young beech
Amaurëa = before dawn