Stannis Baratheon is the younger brother of Robert Baratheon and lord of Dragonstone.
Stannis Baratheon is the middle child of the three Baratheon sons of Steffon Baratheon. In season one, Stannis is mentioned, but never shown. His younger brother, Renly, serves on the small council of his older brother, King Robert.
After Robert's death, and the betrayal of Ned Stark, Stannis makes his claim for the Iron Throne. Stannis claims that because Joffrey Baratheon is the product of incest between Cersei and Jaime Lannister, he is not a Baratheon and is not the rightful heir of the throne. Renly Baratheon also makes a claim to the Iron Throne, although he is behind Stannis in the line of succession. Renly's claim is based on his perceived popularity among the people. Stannis creates his own sigil and house, House Baratheon of Dragonstone, to distinguish from his brother who is using House Baratheon and Joffrey who is using House Baratheon of King's Landing.
In the War of the Five Kings, Stannis seeks advice from Melisandre, a fire priestess who worships the Lord of Light. Stannis confronts his brother, Renly, telling him to renounce his claim to the throne and join his side in battle. Renly refuses and is subsequently killed by a shadow spirit that Melisandre "births."
Along with Melisandre is Davos Seaworth, a former smuggler who urges Stannis to ignore the priestess. Stannis takes Renly's remaining troops and targets King's Landing. Stannis' troops greatly outnumber the Lannister troops at King's Landing. In the Battle of Blackwater Bay, Stannis' fleet arrive at King's Landing, but are met with wildfire, a dangerous substance which destroys much of the fleet. Stannis' troops arrive at the gates of King's Landing, but fail to make it past the gate. Most are wiped out by Tywin Lannister's own troops. Stannis fleas the battle, defeated.