The Seven Kingdoms is the name given to the realm that controls most of the continent of Westeros and its numerous offshore islands, ruled by the King of the Andals and the First Men from the Red Keep in the city of King's Landing.
The name of the realm dates back to the time prior to the War of Conquest, during which seven independent kingdoms existed on the continent. The realm actually consists of nine distinct regions, the remaining two being formally established after the Targaryen conquest, and thus they are not actually considered to be "kingdoms." Regardless, all nine provinces are subject to the rule of the Iron Throne.
The realm became fractured from years of civil warfare with the Kingdom of the North and the Kingdom of the Iron Islands attempting secession. However, the North has pledged to House Targaryen while the Iron Islands have allied with House Lannister, with both sides agreeing to an armistice to deal with the Great War to the north (though secretly, Cersei Lannister and Euron Greyjoy plot to betray the Starks and Targaryens).