The elder son (though third child) of Bregor of the House of Bëor. Bregolas had three children of his own, through each of whom he became ancestor of a famous line. His daughter Beleth (also called Bereth) was a distant ancestor of Erendis of Númenor; his elder son Baragund was grandfather of Túrin Turambar; and his second son Belegund was grandfather to Tuor.
After the death of his father Bregor, Bregolas would have become the head of the House of Bëor. He served with the Elf-lords Angrod and Aegnor in the northern land of Dorthonion, and he was by their side when the forces of Angband launched the sudden and devastating attack that would become known as the Dagor Bragollach. Bregolas died quickly in that assault, but his sons survived to join their uncle Barahir. With Dorthonion under Morgoth's control, they became outlaws in the land of their father.
Notes
1
These dates come from a genealogical chart of the House of Bëor reproduced in volume XI of The History of Middle-earth. They are not therefore strictly canonical, though they do fit with the established timeline of the published Silmarillion.
2
The Etymologies (in volume V of The History of Middle-earth) specifically interpret the personal name Bregolas as 'fierceness', deriving from an Elvish word bregol meaning 'violent' or 'sudden'.
3
The published Silmarillion only mentions the two sons of Bregor: Bregolas and his brother Barahir. The three daughters shown here appear on the more detailed genealogy of the House of Bëor in volume XI of The History of Middle-earth.
4
Most sources (including the text of The Silmarillion) give Bregolas primacy over his brother Barahir, and what dates we have confirm that Bregolas was the elder brother by seven years. The abbreviated genealogy of the House of Bëor in The Silmarillion shows Barahir to the left of Bregolas, but this is presumably a mere question of convenient layout and not meant to show their relative ages.