The WAR who gives you the quests tells you what lore remains. In some cases, "job of eld" means "there aren't many of these in existence, anymore", which naturally means that there's not much information about them left, either.
The Basics
The Roegadyn that settled the far north of Aldenard, the Farreach, came to believe that their highly volcanic region contained the gates to the hells, thus their clan name - the Hellsguard. It's likely that these red-skinned Roegadyn are a recent branch from their Sea Wolf ancestors, as their lore doesn't seem to go back as far and they, too, use the axes common to those of the sea. One might imagine that Sea Wolves came from the north and some opted to stay in the volcanic Farreach, later adapting to become Hellsguard the same way the Lalafell adapted from the plains of the south seas to the dunes of Thanalan.
Their clan spawned a long line of warriors that perfected batting with a different style of axemanship - one that channels an unwieldy and animalistic inner strength that many fail to ever fully control. Over time, they also developed a unique design of armor (which Rowena has since copied), as well as an axe that reflected their discipline - the Bravura, made of metal from the heavens forged in the fires of the earth - whose design has mostly been lost to time. However, the lands of the Farreach aren't very good farmland, so they traveled as mercenaries to return with goods. In recent days, though, many have shunned the old teachings and moved to the cities (especially Ul'dah) to work as common sellswords. These Hellsguard tend to "translate" their names into the Eorzean tongue.
In modern Eorzea, most combat disciplines are basic and highly specialized for regional use; they're formidable, but not powerful enough to combat the threats to the continent. As such, the powerful Jobs of Eld are being resurrected, which has made Curious Gorge eager to restore and spread the teachings of his clan of warriors... if those that would teach it can tame his own inner beasts.