Dengar is a human bounty hunter, one of the six answering Darth Vader's call aboard the Executor in The Empire Strikes Back (1980). StarWars.com is unusually unkind about him and unusually clear about why he works: "Crude and slovenly, Dengar was nonetheless an effective bounty hunter. While some hunters prided themselves on finesse and style, Dengar preferred firepower and destruction."
The bandages
The costume is a swaddle of dirty field dressings around the skull, which reads instantly as head trauma. Every subsequent treatment of the character has built on that: whatever happened to Dengar, it damaged him, and he has been compensating with ordnance ever since.
Payback
Dave Wolverton's "Payback: The Tale of Dengar" in Tales of the Bounty Hunters (Bantam Spectra, December 1996) gives him a Legends backstory as a Corellian with the nickname Payback, flying a ship called the Punishing One. The story leans hard into the head injury as an origin: surgical alteration, suppressed empathy, a grudge, and a man rebuilt into an instrument.
Fett's preferred colleague
The databank notes that "Boba Fett enjoyed working with Dengar and held him in high regard due to his proven track record in hunting down prey", which is about the warmest thing anyone in this profession says about anyone else. K. W. Jeter's Legends Bounty Hunter Wars trilogy (1998–99) opens with Dengar pulling Boba Fett out of the sarlacc's aftermath and nursing him back to health — the pairing that most Legends readers remember.
Canon keeps him working
Current canon has been generous to him. He recurs through The Clone Wars, which places him in the profession decades before the films and puts him alongside Boba Fett, Bossk, Latts Razzi and Embo in the season-four episode "Bounty". That gives him the longest documented career of anyone in the Executor line-up.
What the two continuities share
Very little of Wolverton's specific biography survived the 2014 reset — the Corellian origin, the nickname and the Punishing One are Legends. What both continuities keep is the temperament: a hunter with no code, no elegance and no interest in acquiring either, who is nonetheless first in line every time there is work.
Why he is worth a full entry
Because he is the control case. Strip away the mystique that accreted around Fett and the philosophy that Anderson gave IG-88, and Dengar is what the job actually looks like: unglamorous, violent, freelance, and still going.