Dagmer Cleftjaw was a longtime friend of Balon Greyjoy. When Balon was fifteen the two men sailed together and spent the summer reeving. Dagmer has remained loyal to House Greyjoy for many years, training Balon's son Theon Greyjoy in combat and being one of the few individuals to treat Theon with any kindness. Theon returns the affection and is more fond of Dagmer than Balon and Ned Stark, who he was sent to live with as a hostage combined.
When Theon chose to help his father in the war effort against the starks, Dagmer assisted in his raiders and was persuaded by Theon to follow his plan to take Winterfell, having Dagmer cause a diversion by invading Torhen's square to draw the garrison away from Winterfell, allowing Theon to take it over. Not much is known about Dagmer after this except that he took Berena Hornwood and her children as captives.
The tv version of Dagmer is much more sinister and manipulates Theon into seizing Winterfell, then pressures a reluctant Theon into beheading Ser Rodrik Cassel. When Theon needs to have two children to be killed to pass them off as Bran and Rickon Stark, he tasks Dagmer to do the job. Unlike Theon, who struggles with the things he's done and feels genuine remorse, Dagmer feels nothing but joy and amusement over the pain it caused to Maestar Luwin. When Theon tries to assuage his guilt by asking Dagmer to pay compensation to the farmer the orphans lived with, he learnt that Dagmer has already disposed of the farmer and his wife. In order to survive the sack of Winterfell Dagmer knocked Theon out in order to turn him over to House Bolton and get safe passage home. When Luwin tried coming to Theon's rescue Dagmer stabbed him. Dagmer's betrayal backfires as he himself is betrayed by Roose Bolton's bastard Ramsay Snow who has him flayed alive.