The "Four Kingdoms" was the name given to those portions of the former Province of Anacreon which broke away from the Galactic Empire in the early years of the Foundational Era, to form independent and short-lived kingdoms. The largest and most powerful was Anacreon itself.
The Four Kingdoms were the immediate neighbors of Terminus in the early years of the Foundation, during the time of Salvor Hardin. As such they were located at the extreme edge of the Periphery of the Empire. They rapidly descended into a "barbarous" state with petty nobles fighting meaningless wars, and technology declining to the point that knowledge of advanced nucleics was lost. Following the breakdown of widescale communications in the Periphery, for a time the Four Kingdoms represented all of known space in regular contact with Terminus.
Salvor Hardin addressed the First Seldon crisis though manipulating a balance of power. If any one of the Four Kingdoms conquered Terminus it would gain such a technological advantage over the other three that it would easily destroy them. Hardin therefore warned the other three kingdoms when Anacreon tried to establish a presence on Terminus, after which they joined in a coalition protesting Anacreon's move, after which Anacreonian forces withdrew rather than face all out war. Eventually, Anacreon grew so powerful that even the other three kingdoms combined could not act as a deterrent against it, but by this point the science-cult of the Foundation had spread so thoroughly in the Four Kingdoms that their own soldiers dared not attack Terminus.
The Four Kingdoms were soon absorbed into the Foundation itself. In later generations the phrase "Four Kingdoms" remained as a physical term for that region of the galaxy, which in time became the core territories of the ever-widening Foundation sphere of influence. Hober Mallow was himself from Smyrno, while Han Pritcher was born on Locis to Anacreonian parents. The campaign of General Bel Riose, representing the last gasp of the Galactic Empire, proved a dire threat to the Foundation's survival, and even managed to penetrate as far as the Four Kingdoms. At the campaign's high water mark, Riose even managed to capture Loris - but he was soon recalled to Trantor to be executed as a threat to Emperor Cleon II.
Asimov did not give a consistent listing of all the Four Kingdoms. "The Encyclopedists" and subsequent entries clearly state that Anacreon and Smyrno form two of the kingdoms, as they have recently been at war with each other. "The Encyclopedists" also makes passing mention of the planets Konom and Daribow as possible threats to Terminus now that the Periphery is collapsing, but these names are never mentioned again. By "The Merchant Princes", however, Asimov mentions that one of the other kingdoms was Loris. In "The General" the text explicitly states that Loris was one of the original Four Kingdoms. The identity of the fourth kingdom, however, is not entirely clear: it is possible that Asimov originally intended Konom and Daribow to be the third and fourth kingdoms, but later retconned the name of the third to Loris. Alternatively, Konom and Daribow are only mentioned at the very beginning of the breakdown of authority in the Periphery, before the "Four Kingdoms" become formally established after several decades. It is possible that alternatively Konom or Daribow was another petty kingdom which was quickly absorbed by one of the other four. It is also conceivable that the fourth kingdom bore a double name: "Konom-and-Daribow".