The Kingdom is the Monarchical Government of Galaluna under the Rule of The King's Family blood line. Like The King, its proper name is currently unknown, however, The King does reference his government as "The Kingdom" in Escape From Galaluna.
It is unknown how long The Kingdom has existed but from what we saw in flash backs the nation has prospered. The Kingdom's major enemy is the Mutraddi who they defend Galaluna from. The Kingdom was known as a passive nation who avoid war and instead focused on technology, like the Rift Gate created by Edward and the Octus unit by The King.
Thought it is unknown the current time/era/etc.. of Galauna, right before Ilana, Lance, and Octus arrived on Earth the Mutraddi attacked Galauna with a surprise attack. Lance tried to warn The King about the attack but was restrained by the Galalunian Commander who was working for General Modula, a thought to be dead Galalunian military general who seeks revenge for being left behind at a previous Galaluna/Mutraddi battle. At this point it is clear that General Modula is throwing a coup d'etat (over throwing the government) and being assisted by the Mutraddi, however, it is unclear if Modula is the leader or being controlled by the Mutraddi.
With The Kingdom imitate danger The King sends Ilana, Lance, and Octus away to ensure The Kingdom and the blood line continues. The King promises to call Ilana when he wins, however, if he loses it is up to the trio to lead their people to freedom.
At this time The Kingdom is controlled by Modula and The Resistance is working to overthrow the Mutraddi.