Officially, they are focused on protection of good faith in private affairs (where 'private' is defined broadly as 'magical society'). Their name comes from an epithet used for Jupiter. They began as a society a few years after The Pact, out of an older secret society that was more explicitly "we are the lords of the land and all we survey". About four-fifths men, and the women they invite tend to be very accomplished and well-born.
“Dius Fidius is - well. Before the Pact it was the landholders, the Lords of the Land, who held the magic in their tight little fists. Some of them more nobly than others. The official line is protecting good faith in private affairs, but you can see how that goes without me telling you. Half the men in first class likely aspired to it.”