Final Fantasy games feature special attacks, unique to each party member, with mechanics that vary from game to game. (Think of the continuity between games in the Final Fantasy series as having familial resemblance: there are repeated features, but no guaranteed shared qualities or mechanics beyond turn-based battle systems with multiple characters linked to the player. Rarely do games share a universe, and thereby causal and narrative links.) The Limit Breaks are the special-attack flavor of FFVIII, intended as a double pun: you can 'hit your limit,' where your character reaches a very low level of hit points; and you can 'break past your limit', and initiate an attack beyond the ordinary potential of the character. For Quistis Trepe, that means one of several blue magic spells.
I want to say a little about that, but first, a little ground work:
Magic is color coded in Final Fantasy, conveniently enough. Typically there is some mixture of white magic and black magic in any given game, opposed in the sense that white deals in healing and buffing, black with damaging and de-buffing. (There's also time and green magic as well, but they're less relevant for the contrast, so let's just sweep them under the rug, eh?) There is an implicit connection to 'life' in white magic; it damages the undead, for example, suggesting that white magic aids the living, harms the non-living. (Sometimes white magic is connected with an ability to summon enchanted creatures to one's aid, which arguably strengthens a claim that white magic is the life magic, if it can summon particular varieties of life..) Black magic, in contrast, features at least four elements from the traditional Greek building blocks of the world: fire; water; air; earth. These elements pair off, such that each element is strong against another element, weak if that selfsame element is used against it, and normal when paired with any other. It may even heal if applied against a creature that shares that elemental type. Usually these two types are acquired through the game's normal learning mechanics, typically awarded through gaining levels through quantified amounts of experience, and though every game has a player-connected character with black magic capabilities, white magic is inevitably 'good guy' magic. Rather often: 'good girl' magic.
In contrast, blue magic's nature and acquisition is linked with the creatures of the world. (Notably not the big-bad villains, but the standard issue enemies you encounter in various areas.) Gaining abilities is not a matter of progress through levels, but rather through chance encounters with particular enemies, or procuring rare items. In contrast to the quantified experience – you knock out a few baddies and are awarded experience points depending on the difficulty and number of these enemies – blue magic is usually dependent qualitative experience. That is, you the player have to know something about the world (where are the enemies or items that offer this ability?) in order to gain the abilities, regardless of character level. Think of it as magic of the world, neither manifestly good or bad, as the world is neither good nor bad. Now while black magic isn't 'bad' magic, white is almost always good magic; it can only help you, and when magicality is specified as a part of characterization, only good characters possess it. It harm enemies, or help the party, and usually the animation of the ability retains features of its creature origin – Quistis's bad breath from the dreaded Marlboro, for example, is a putrid belch of green gas. If white magic is never seen in the hands of the enemy, blue magic is the petty enemy's strength turned back against them.
Quistis is a blue mage, as said. There is no in-game conversation which details her reasons for that Limit Break, but it is fertile ground for interpretation. Notably, it is very unsexy. (Belch of green gas, like I said.) But as I said it is also magic of the world, which involves an active interest in mirroring the capabilities of the creatures that slash and hack at you, and I think of that as a kind of studied empathy. It is also, if the player's travails in acquiring the abilities count, difficult magic. You need specific and rare items to master it. Though the nature of limit breaks (they happen as a result of probability when a character's hit points reduce to a certain number) seems removed from the narrative of the game, they do seem connected with the nature of the characters in such a way that they don't seem removed from the story. Zell and Squall's combat-flourishes, for example, you could imagine cinematically: in a flash of inspiration during extreme weakness, you use your most devastating but unpredictable techniques. That says something about how their characters perceive desperation. What Quistis chooses to offer when the chips are down is an arsenal of curiosities. Not quite so random as Selphie's spinning slot of possible magics, or an attack typical except for potency, as with the male party members.
When the going gets weird,
the weird turn pro
Fear and Loathing at
the Super Bowl
You could take it as Trepe being a spaz at the worst possible moment, but I find it so endearing that she pulls out oddly specific monster-moves when she fears for the worst. It's obscure, and learnéd, and involves empathy with creatures beyond the scales of morality. It’s totally undignified. It suggests that Quistis Trepe (like Rinoa) does not solve problems through the same technique, though more of it, but by doing something entirely different.