Aegis War: The war that raged between Mythra and Malos 500 years ago. It sank 3 giant Titans forever to the Cloud Sea's bed.
Architect: Klaus, the mad scientist that split his original world in half, created this world.
Artifice: Servants of the Aegis, controlled by them. A.k.a. war machines. Mythra used to have Ophion and Siren; while Malos had quite a lot of them.
Blades: Crystals summoned such living beings to help them fight, by either lending their power to their Drivers, or fighting themselves.
Cloud Sea: The surface of Alrest is filled with a sea of clouds, beneath which is an ocean.
Core Crystal: Unactivated ones could be used to summon a Blade. When their Drivers die, the Blades returned to their Core Crystal, waiting for their next master. Upon resummoning, Blades' memory with their previous master will be totally wiped clean, for every return to the core crystal means a factory data reset. But when they see their masters, if their previous masters cared for them greatly, tears could still roll down their cheeks and they don't know why.
Elysium: The supposed heaven atop the World Tree where people lived in harmony and peace; a utopia.
Fonsett Village: The place where Rex was born and raised up.
Gormott: The place where Nia (a Gormotti) was born and raised. The striking feature is cat ears. The city on Gormott is Torigoth. Gormott is an annexed country of Mor Ardain.
Salvager: You'd expect, living in a world consisted mostly of sea, that the richest materials would also be in the sea than on land. The old cities of Klaus had sunken beneath the ocean floor, and salvagers took advantage by salvaging them up again. Oh, and also supplies from other sunken Titans: when they die, their supplies goes down to sea bed with them, whatever's not quick enough to move to another Titan.
Titans: the only creature that could brave the cloud sea by forever floating above. The giant ones, people built their cities on them. The small ones, like Gramps, only support barely one person. But titans also gets old, and when they do, they sink beneath the cloud sea, bringing the entire city with them. When Titan's dead, they produced a Core Crystal. The most giant of them all today only have three: Mor Ardain, Uraya, and Indol. In the past, there are more, including the sunken golden country, Torna.
Torna: The original Torna was a Titan, but it was sunk 500 years ago, during the Aegis War. The new Torna was created by Jin, a terrorist group that raided Core Crystals, their aim to go to Elysium.
World Tree: Supposedly holding Elysium, the heaven where people lived; but no, it's some factories where Klaus half-body were found, and nobody else there (except the non-living robots). The heavens were some deserts of dead plants and old-world remains, in dilapidated forms.