The War of the Five Kings was a large, multi-theater conflict fought in Westeros from 298 AC until 300 AC, and culminated in the arrival of Aegon VI Targaryen and the attacks of Euron Greyjoy. 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, with Robb claiming the titles of King in the North and King of the Trident and Balon claiming to be King of the Isles and the North.
Though many name the war as having ended with the deaths of Balon and Robb, and the defeat of Stannis at the Blackwater, many maesters name the official end as Aegon's landing in Westeros - dividing the War into three separate conflcits called the Second War of Conquest, which included the War of the Reach, and the Winter War.
For more information about the War of the Five Kings, see this page on the ASOIAF Wiki. Our canon takes over where the War ends, meaning all that had previously occured is therefore canon.