During the War of Conquest, he was a commander in the army of Aegon the Conqueror, and was the Conqueror's bastard half-brother. When Aegon invaded Westeros, he sent Orys to seize Storm's End, the ancestral seat of the Storm Kings and capital of the Stormlands. Orys defeated the Storm King, Argilac the Arrogant and took not only Storm's End but also his sigil - the black stag - and words - "Ours is the Fury - as well as his daughter Argalia, to cement his rule over the Stormlands. He became the first Lord Paramount of the Stormlands. 
He has an entry in The Lineages and Histories of the Great Houses of the Seven Kingdoms which reveals that he married Argalia, the daughter of the last Storm King, Argilac the Arrogant.
In the books
The World of Ice and Fire reveals that Orys Baratheon was Aegon's closest friend and ally. He served Aegon as the first-ever Hand of the King. Aegon offered Orys's hand in marriage to the daughter of the Storm King, Argilac Durrandon, but was rebuffed. Angered at the insult of being offered a bastard instead of a king, Argilac cut off the hands of Aegon's envoys.
When Aegon landed his army at the mouth of the Blackwater Rush, he led a lightning campaign to secure the surrounding area, taking Rosby, Stokeworth, Duskendale and Maidenpool in short order. Orys led the army while Aegon attacked from the skies.
After this victory, Aegon sent Orys and his sister-wife Rhaenys to take Storm's End. Argilac left his castle to give battle in the open, attacking during a torrential thunderstorm to limit the use of Rhaenys's dragon, Meraxes. However, Meraxes instead fought on foot and was still able to inflict carnage on Argilac's forces. Argilac himself was slain by Orys. Orys negotiated the surrender of Storm's End, with Argilac's daughter Argella delivered to him in chains and naked. Orys treated her kindly, later wedding her.
Orys continued to serve as Hand of the King for his nephew Aenys I, who succeeded Aegon I upon his death. Orys later died during one of the numerous local rebellions against Aenys I: many lords hoped that with Aegon the Conqueror dead and his weak son on the throne, they might be able to throw off Targaryen rule forever. These rebellions were crushed by Aegon's ruthless younger son, Maegor the Cruel, who succeeded Orys as Hand of the King.
The relationship between Aegon the Conqueror and Orys Baratheon may be loosely inspired by that of the real-world William the Conqueror of Normandy and Odo of Bayeux, whom like Orys Baratheon, was the Norman conqueror's half-brother and vassal, and upon the conquest of England, was made the ruling earl of an important region of England and was his brother's regent and chancellor in that country.
|Lord:||King Stannis I||Heir:||Princess Shireen Baratheon|
|Seat:||Storm's End||Lands:||The Stormlands|
|Title(s):||Lords Paramount of the Stormlands · Lord of Storm's End|
|Ancestors:||Durran Godsgrief · Argilac the Arrogant · Orys Baratheon · Argalia Baratheon · Monica Baratheon · Mychal Baratheon · Axel Baratheon · Lyonel Baratheon|
|Deceased members:||Renly I · Robert I · Steffon Baratheon · Cassana Baratheon|