Like humanity's creation myth, the nature of magic is contained in oddly oblique instances, though you begin using it almost immediately upon having the junction system explained to you in a tutorial. Final Fantasy games often make use of a summoner or a summoning class, where a character has the ability to call certain monsters to their aid; they also usually feature a system of equipment which you can equip or remove from your characters to manipulate their stats. FFVIII combined these features into the aforesaid junction system. Once you obtain Guardian Forces, you can pair those Guardian Forces to particular characters. Not only can the characters elect to summon their paired Guardian Force into battle, but depending on the abilities of that Guardian Force and the character's store of magic, their stats can be buffed, and that character can enjoy abilities exclusive to that Guardian Force. All Guardian Forces, however, have the ability to draw magic. In battle, this means pulling magic out of a person or monstrosity, but there are occasional 'natural' draw points lying about. Using this 'draw' ability allows your characters to store magic, which then allows you you to 'attach' it to particular stats to increase them, with results varying with the stat, and with the type and the amount of magic available.
Eventually you encounter the inventor of the junction system, Doctor Odine, a figure seemingly committed to research above the bounds of moral compunction. Though initially interested in the nature of the hostile monsters roving the world, a project which introduced him to the peculiarity of Guardian Forces, the doctor was recruited by the Sorceress Adel to lead certain research projects on her behalf, one dealing with the search (and later the study) of her intended successor, and one dealing with focusing monsters as a way of weaponizing them. Conducting these projects also enabled Odine to study Adel with her permission, and so enjoy an unrivaled access to studying the nature of magic. The game doesn't make the chronology clear beyond this, but those disparate research projects led Odine to discover, perhaps invent, para-magic. Sorceresses and monsters possess and manipulate natural magic. The junction system allows a character to wield magic via an intermediary - a Guardian Force - where the magic obtained and stored is para-magic.
It's unclear whether the junction system is a device or a technique. As with any game, it's difficult to tell whether certain arbitrary rules are products of the interface, or usable evidence in determining the nature of the world. Does the fact that one can only store up to 100 units of 32 different types of magic strike you as device-like? It strikes me that way, yet the informational panel in Instructor Trepe's classroom, an in-game device used to tutor students at the Balamb Garden military academy, alludes to junctioning as a technique, and magic as a manipulation of energy. Almost identical information is eventually available in the interface for your perusal, so you have your choice of lore: data, or meta-data.
Setting aside that ambiguity, I want to elaborate on three areas of research for Dr. Odine: Guardian Forces, and what makes them distinct from the ordinary run of monster; his research on Adel's intended successor, a young woman named Ellone; and Adel's hopes for weaponizing monsters.
In his early research, Dr. Odine noticed that certain types of monsters were capable of sharing consciousness with people who have similar consciousnesses, one aspect of what it means to junction. Though the game certainly notes that only particular monsters are capable of this consciousness sharing, it is not as clear if it also means that only certain people have the right types of consciousness that enables sharing. (The interface tracks your compatibility with any given Guardian Force, which shrinks or lengthens the time to summon them in battle. This could be the intended level of 'similar consciousness', yet it might be more significant.) That sharing of consciousness means more than the person in question being able to direct the abilities of the Guardian Force, say by summoning, or equipping some of that Guardian Force's ability to themselves - in fact the Guardian Force loses any corporeality beyond brief appearances when summoned. Interestingly, sharing consciousness in this way has the negative effect of causing memory loss in the person they junction to, seemingly a cumulative effect of junctioning to any number of Guardian Forces over time.
Consciousness-sharing doesn't seem to simply be a product of these monsters. While working for the Sorceress Adel, Dr. Odine became involved with the search for her successor. Becoming a sorceress is the result of inheriting that sorceress power from a dying predecessor; given the unnatural longevity and hardiness of a sorceress, however, 'dying' is almost certainly the result of wounds inflicted during battle, and the predecessor is compelled to transfer their power to any nearby woman with the right capacity. Adel notes that this capacity is discernable if you know what to look for, and the young woman Ellone evinces it. However, Ellone has the seemingly unique ability to send a contemporaneous consciousness backward in time, attaching it to the consciousness of a person in the past. Although the future-person doesn't seem to be able to meaningfully impact any decisions of the past-person, comments by Laguna Loire on periods when his future son, Squall Leonhart, was attached to him suggests that the future-person adds their strength to the past person. Specifically, he notes the surge of power as having 'fairies' on his side. The future-person has no corporeal presence when so attached.
How incredibly like the junctioning of a Guardian Force to a person.
Independent of Adel's plans for Ellone, Dr. Odine constructs a machine capable of this same sort of consciousness attachment, which he names the Junction Machine Ellone. As this machine becomes more sophisticated over time, the primary antagonist, the future sorceress Ultimecia, begins to use it to manipulate the past.
Before I speculate on what this bears on the nature of sorceresses, I want to call attention to one last branch of Odine's research. Though the game offers loving cinematography of the moon during key narrative moments, the significance of these shots is chalked up to romantic imagery until the plot reveals that the moon teems with monsters. At certain orbital points, these monsters funnel to the planet below, an event termed a Lunar Cry. Given the cyclical nature of orbits (#literally), Lunar Cries have always occurred, and will always occur, and they bring incredible destruction in their wake. The Centra civilization on the eponymous southernmost continent was so destroyed, though the precise date of the destruction is unclear due to conflicting information (4000 years ago, versus 80 years ago, is quite a bit of difference). While under Adel's rule, Esthar discovered an enormous object believed to have fallen from the moon, the crystal pillar. Independent orbital positioning, the crystal pillar could initiate a Lunar Cry due to the 'energy' field it creates between itself and the moon; thus Adel sought to weaponize it by housing it in a mobile fortress, the Lunatic Pandora, which could be moved to enemy locations and engaged, bringing down a rain of monsters to the desired area.