The Queen of Andor is the ruler of all of Andor. This Kingdom is ruled only by women and so can be considered a Queendom.
After a Queen dies without a sure heir (a proclaimed and recognised Daughter-Heir) or is deposed, a woman who wants the throne must get approval by the majority of the noble houses of Andor, which was eleven great noble houses at the time of the Dragon Reborn.
During the history of the Qeendom of Andor there have been many Succession Wars to establish the right of a noblewoman to rule.
The queens (since Ishara the first one) have usually sent their Daughter-Heirs to the White Tower to seek training and guidance before succeeding on the throne. Also, the queen's eldest son would also be sent to the White Tower to gain military training as Warder before claiming the post of First Prince of the Sword.
There have never been Kings of Andor, and Queens of Andor are full queens regnant.
Queens during the War of the Hundred Years