DaiMon was a quasi-military rank in the Ferengi Alliance. A DaiMon was roughly equivalent in rank to a Starfleet Captain. The title was usually purchased, and a DaiMon would either be commanding a Ferengi starship or would be assigned to an equivalent political or military posting.
The Ferengi Alliance empowered DaiMons to enter into trade agreements on behalf of the Alliance, including new trade routes and agreements. They also had the authority to speak for the Alliance itself - even for high officials such as the Grand Nagus. (TNG episodes: "The Last Outpost", "The Battle")
DaiMons were required to give sizable percentages of their claims to the Grand Nagus and the GuiMon in Chief. Occasionally a DaiMon could use a large discovery as leverage to demand a higher percentage. (TNG - The Lost Era novel: The Buried Age)