King Rhoam Bosphoramus Hyrule is a character in The Legend of Zelda: Breath of the Wild. He is the former King of Hyrule as well as the father of Princess Zelda, he is the first person that Link encounters after awakening in the Shrine of Resurrection, under the guise of a simple Old Man.
For the moment King Rhoam's role in the Zelda series is only composed of informations with an unconfirmed timeline placement and should stay this way until we have a definitive answer, so please don't add any information regarding the timeline placement without OFFICIAL confirmation, thanks.
17 years before the Great Calamity
King Rhoam and the Queen of Hyrule had a child, a daughter, who in the traditions of the royal family was named Zelda.
11 years before the Great Calamity
the Queen of Hyrule died unexpectedly, putting the King and Zelda in great shock. A royal funeral was held, where King Rhoam noticed that his daughter never cried. This is said to be due to her being raised by her parents to be a valiant and steady princess. Her strength was said to have given the King hope. He then chose to raise Zelda to adulthood on his own.
100 years before the events of Breath of the Wild
the people of Hyrule discovered various ancient artifacts, some of those confirmed the existence of Calamity Ganon who was tought to be a myth up until now. this discovery led King Rhoam to insist that the relics be investigated as thoroughly as possible in order to prepare for his inevitable return. King Rhoam and Zelda then choosed four champion to pilot the four Divine Beast in hope of fighting back against Ganon when he would appear, those champions were found in the person of Princess Mipha (for the Zoras), Revali (for the Rito), Daruk (for the Gorons), Urbosa (for the Gerudo).
When Calamity Ganon attacked, King Rhoam aided with the effort of pushing him back along with the aid of the four Champions and the Divine Beasts. However, Ganon was cunning and created blight Ganons to take control of the Divine Beasts and turn the Guardians against the King and his people. On that day those inside Hyrule castle, the Champions, and himself, all lost their lives. Princess Zelda, the king's daughter, survived and managed to seal away Ganon for a time. Though dead, Rhoam had since wandered the wild as a spirit, concealing himself in a brown cloak.
During Breath of the Wild
A hundred years after the Great Calamity, his daughter's spell beginning to wane, Rhoam encounters Link when he arrives to the Great Plateau, giving him some quests to complete under the identity of the Old Man. Once Link completes the quest of entering the four Shrines on the Great Plateau, Rhoam reveals his identity to Link and proceeds to tell Link of the tragedy that had befallen Hyrule one hundred years ago. Rhoam then tells Link to make his way east toward Kakariko Village and seek out Impa, as heading off directly to Hyrule Castle right now in his current condition would be quite reckless.
Following Ganon's defeat, King Rhoam sees his daughter one final time before he and the Champions depart.