The War of the Five Kings was a large, multi-theater conflict fought in the Seven Kingdoms from 298AC until 300AC. As the name implies, over the course of the war five men claimed the title of king: Joffrey Baratheon, Stannis Baratheon, and Renly Baratheon all claimed the Iron Throne, whilst the separatists Robb Stark and Balon Greyjoy attempted to secede their lands from the rule of the Iron Throne, claiming the titles of King in the North and King of the Iron Islands respectively.
The War of the Five Kings is the principal military conflict depicted in the first three novels of the A Song of Ice and Fire series, and its aftermath and successor conflicts continue in the latest two novels. According to Archmaester Benedict, the name of the conflict is incorrect because Renly Baratheon was slain before Balon Greyjoy crowned himself, so there were never technically five kings at once.