"...the Baratheons fight each other, ..."
House Baratheon of Storm's End was one of the Great Houses of Westeros, although also one of the youngest. It is the current royal house.
House Baratheon's sigil is a black stag on a gold background and their house motto is "Ours is the Fury". When Robert ascended the Iron Throne, a gold crown was added to the stag, denoting their status as the royal house.
The ancestral Baratheon stronghold is Storm's End, but since becoming the royal house, they have also taken possession of the old Targaryen island fortress of Dragonstone, while the King rules from the city of King's Landing, the capital of the Seven Kingdoms.
When the War of the Five Kings began following King Robert Baratheon's death, House Baratheon became divided into three distinct factions: one led by Robert's alleged son (who is actually the product of an incestuous relationship between Cersei and Jaime Lannister), Joffrey; one led by his younger brother, Stannis; and one led by his youngest brother, Renly. As a result of Renly's murder and the casualties suffered at the Battle of the Blackwater, the majority of House Baratheon's surviving lords and bannermen are now sworn to Stannis, though much of the Stormlands are occupied by Lannister and Tyrell forces loyal to King Tommen Baratheon, Joffrey's younger brother and successor.
After the deaths of Stannis and Shireen, Tommen is the last remaining official member of House Baratheon - though in reality he is not a Baratheon at all, but Jaime Lannister's bastard son. The only remaining known member of the actual Baratheon bloodline is Gendry, King Robert's unacknowledged bastard son.