To our neighbors, Ferelden seems utterly chaotic. Unlike other monarchies, power does not descend from our throne. Rather, it rises from the support of the freeholders.
Each freehold chooses the bann or arl to whom it pays allegiance. Typically, this choice is based on proximity of the freehold to the lord's castle, as it's worthless to pay for the upkeep of soldiers who will arrive at your land too late to defend it. For the most part, each generation of freeholders casts its lot with the same bann as their fathers did, but things can and do change. No formal oaths are sworn, and it is not unheard of, especially in the prickly central Bannorn, for banns to court freeholders away from their neighbors--a practice which inevitably begets feuds that last for ages.
Teyrns arose from amongst the banns, warleaders who, in antiquity, had grown powerful enough to move other banns to swear fealty to them. There were many teyrns in the days before King Calenhad, but he succeeded in whittling them down to only two: Gwaren in the south, Highever in the north. These teyrns still hold the oaths of banns and arls who they may call upon in the event of war or disaster, and similarly, the teyrns still hold responsibility for defending those sworn to them.
The arls were established by the teyrns, given command of strategic fortresses that could not be overseen by the teyrns themselves. Unlike the teyrns, the arls have no banns sworn to them, and are simply somewhat more prestigious banns.
The king is, in essence, the most powerful of the teyrns. Although Denerim was originally the teyrnir of the king, it has since been reduced to an arling, as the king's domain is now all of Ferelden. But even the king's power must come from the banns.
Nowhere is this more evident than during the Landsmeet, an annual council for which all the nobles of Ferelden gather, held for almost three thousand years except odd interruptions during Blights and invasions. The sight of a king asking for--and working to win--the support of "lesser" men is a source of constant wonder to foreign ambassadors.
--From Ferelden: Folklore and History, by Sister Petrine, Chantry scholar