OK, now that I'm back from doing laundry...
Key Points
Ivalice
An ancient kingdom, in contemporary times it is considered only legend. Once home to a corrupt aristocracy, the commoner Delita rose to kingship with the aid of Ramza Beoulve and brought forth a golden age; however due to further complications Ramza's name and deeds were stricken from history (see Ultima below); other than the Durai Reports, which chronicle the true history of Ivalice, Ramza is a forgotten figure.
The Clockwork City of Goug, one of the raid dungeons, appears to have been the ancestral homeland of the Garleans.
Ultima, the High Seraph
A seemingly extraterrestrial primal-like being, Ultima is the source of auracite and the main antagonist of the storyline. It was summoned / empowered by one Saint Ajora Galabdos, an ancient Warrior of Light who betrayed Hydaelyn. In order to keep Ultima sealed beneath the Orbonne Monastery, Ramza sacrificed his life and asked his name be stricken from history so as to prevent curious souls from waking the creature. In order to truly break the seal, a Warrior of Light is needed due to Saint Ajora's pact with it. Though sealed at first, due to it spreading pieces of auracite it still retains an influence in the world, and the Durai Reports indirectly led to its (very temporary) release and ultimate defeat.
Auracite, a mineral created by the being, is seemingly capable of storing memories and/or mutating creatures. This is what's responsible for the lucavi, who make up the bulk of the bosses encountered in the raid series. (The Garleans appear to be using a synthetic equivalent to help pilot their new Weapons in the Sorrow of Werlyt arc.)
Dalmasca
A city-state in Southeastern Othard, under which lies the ancient capital of Ivalice, Lesalia. After it was conquered by the Garlean Empire some 30 or so years ago it rebuilt, but in the wake of Doma and Ala Mhigo's successful rebellions made its own bid for freedom. Unfortunately, the response to this rebellion is swift and decisive; Dalmasca is carpet-bombed into submission before long.
A resistance known as Lente's Tears yet lingers, helmed by one Princess Ashe, who was thought to have been killed during the invasion. She uses Fran, a viera, as an ambassador. Ba'gamnan, a former Dalmascan fusilier, is crushed by his guilt at failing to protect Ashe and her brother Rasler during the invasion, which drives his actions and hatred of the Garlean Empire.
The city-state is currently ruled by Noah van Gabranth of the IVth Legion.
Majestic Imperial Theater Company
A theater troupe from the Garlean Empire, now fallen on hard times due to Varis' censorship of the arts. Led by Jenomis cen Lexentale (a.k.a. Arazlam Durrai), who seeks to clear his ancestor Orran Durrai's name and bring to light the truth of Ivalice's existence and history. With him are his two children, Ramza bas Lexentale and Alma bas Lexentale, named after two key figures in Ivalice's history so as to prevent Jenomis from forgetting his life's mission. Unfortunately Jenomis gets in a bit over his head before the story begins, prompting Alma to seek out a hero to save him, which ends up being the Warrior of Light. Their base of operations is their airship, the Prima Vista.
The endeavor is aided by Cid nan Garlond, a Sharlayan scholar by the name of Mikoto, and two moogles, Montblanc and Hurdy.
Questions?