Balon Greyjoy was Head of House Greyjoy and Lord of The Iron Islands. He Was also a very ambitious and ruthless Man. Balon Declared himself King Of The Iron Islands and Rose in rebellion against King Robert Baratheon in order to revive The Old Way ( a lifestyle of Reaving and Plundering). His two eldest Sons Rodrik and Maron were killed in the rebellion.
Balon blamed Ned Stark for his son's death. In exchange for being able to remain Lord of The Iron Islands, Balon and Robert worked out a deal where Balon's youngest child Theon would remain in Winterfell with Ned to insure Balon's good behaviour.
In Theon's absence Balon allowed his daughter Yara to become a warrior and a ship's captain (which was unusual for IronBorn) in order to win his war against the Lannisters Robb Sent Theon to Pyke, hoping Theon could sway his father to their side.
When Theon arrived Balon treated Him coldly, resenting him for his bond with The Starks and Revelated. He planned to attack The North in vengeance. Balon pointed out how the Starks killed his brothers. Theon then correctly countered that Balon's actions were what got him taken hostage in the first place. Balon struck his son across the face.
In a bid gain his family's acceptance, Theon joined his father's rebellion and attempted to seize Winterfell, however he was betrayed by his fellow Ironborn and handed over to Roose Bolton's men. Balon received a letter from Roose's bastard Ramsay Snow, who'd been torturing Theon, the letter Explained that unless Balon withdrew his troops from the North and gave up all occupied territories, Theon's torture would continue.
The letter also came with a box of Theon's severed Penia. Balon refused to help, seeing Theon as useless now, he could not further the family line. However Yara defied her father's orders, attempting and failing to rescue Theon. Balon then chided her for wasting good men in the rescue attempt, in the argument Balon threatened to father a fifth child just to disinherit Yara, then stormed out. He was then killed by his brother Euron, who wanted the Salt Throne.