In the Ferengi language, DaiMon translated to "Captain"; the position was also the equivalent that of a captain. (ENT: "Acquisition"; TNG: "The Battle") In at least some respects the rank could be more precisely compared to the (permanent) rank of Commodore.
DaiMons were authorized to explore new trade opportunities on behalf of the Alliance, and were often empowered to speak on behalf of the Alliance in such matters. (TNG: "The Last Outpost", "The Price") Their duties included reporting to the Ferengi Council. (TNG: "Force of Nature")
The primary agenda of the DaiMon was to earn a profit. (TNG: "The Last Outpost", "The Battle") In fact, according to Doctor Farek, "a true DaiMon would not be blinded by lust," during their pursuit of profit. (TNG: "Ménage à Troi")
The simple misdeed of engaging in an unprofitable venture could lead to them being stripped of their command. Revenge was highly frowned upon, and evidence of one being unstable and dangerous, could result in prison time. (TNG: "The Battle", "Bloodlines")
In 2366, Federation starship Captain Jean-Luc Picard threatened to report DaiMon Tog for kidnapping a Federation ambassador and two Starfleet officers to his superiors, indicating that those superiors "may question your competency as DaiMon." (TNG: "Ménage à Troi")
A non-Alliance affiliated group of privateers, led by an individual who still possessed the rank of DaiMon, were in business for themselves when they captured the USS Enterprise in 2369, hoping to sell it to the Romulans. Upon their failure, and due to their involvement in a criminal activity, their actions were quickly disavowed by the Ferengi government. (TNG: "Rascals")