Geodessima is a science fantasy game, as opposed to the classical/European fantasy setting of Rune Factory. While this distinction does influence the story, characters, and game mechanics, it is largely cosmetic, primarily affecting the nomenclature used throughout the game. In terms of the general player experience, the game stays true to the norms and conventions established by that series and others like it.

The game takes place at an undisclosed point in the future, where personal space travel is commonplace. Hollow asteroids, referred to as Geodes, have been discovered throughout the galaxy. Despite their apparent lack of mass, their interiors contain extraordinarily dense space, giving them Earth-like gravity on their surface and distorted geometry in their interior. This compact coalescence of space, something superficially similar to black holes, is the confluence point of an unknown number of alternate, coaxial universes. Using a specialized tool known as a tuner, it is possible to access these alternate universes, collectively referred to as The Unda. People who explore these alternate universes are known as Muses.

When new Geodes are discovered, they are transported to an empty region of space where small, artificial solar systems, called Geospheres, are constructed. These Geospheres — composed of one or more Geodes orbiting an artificial star — all collectively orbit a space station known as The Omphalos: a hub space that allows for socialization and trade. In game terms, The Omphalos is the town where the player meets and interacts with the game's various characters, in addition to buying various goods and services.

Because alternate universes are coaxial, their spacetime only overlaps at specific points. This has various consequences: For one, only small pockets of these universes, called Stanzas, are normally accessible from a Geode; for another, movement within The Unda does not necessarily correlate to movement in the main universe, meaning that the passage of time is not fixed. In the case of free verses, i.e. randomly generated dungeons, time does not pass in the main universe while the player is exploring.