The suggestion appears to be that Kyber crystals are an exotic form of solid degenerate matter.
Astrophysical theory holds that White Dwarf stars, which begin as fluid masses of ordinary degenerate matter, eventually cool and crystallize into solid degenerate matter, in the process becoming Black Dwarves (theory also tells us that the earliest White Dwarves in the universe have not had time to cool to Black Dwarf stage.)
Degenerate matter is organized so that all electrons occupy densely-spaced, minimal, non-overlapping energy states normally caging an alarming amount of ordinary nucleonic matter. A teaspoonful of White Dwarf matter, you may have heard, weighs 5.5 tons. 99.995% of that mass though, is the ordinary-matter nucleons trapped in a degenerate-electron matrix. The electrons in that teaspoon weigh a mere 8 ounces.
In theory a degenerate substance could exist that's all electron matrix and no nucleons. That's because the electrons don't need the nucleons in order to form a degenerate gas, so long as half the electrons are positively charged antimatter positrons. A 50/50 mix of the two would tend to remain stable because the electrons and positrons are reluctant to approach one another any more closely than they already do.
It could even exist under ordinary conditions; For although created through terrific pressure, the degenerate matrix actually needs more energy to expand once formed than it can absorb from its environment. Its density, about 46 grams/cc, would be low enough you could handle it like an ordinary object merely twice as massive as platinum.
Such an all-electron degenerate matter crystal would have useful properties. You could channel enormous amounts of energy into it and out of it and use it as a perfectly efficient photon emitter. If you pushed it hard enough, it would implode into an instant antimatter explosion yielding 551-keV gamma rays, which could be used to pump an x-ray laser.
Where would you find Kyber? Most likely on a planet formed from a ruptured degenerate star. A crystallized star would tend to rupture if ordinary matter accumulated on its surface until the overburden pressure (the weight of the piled-up matter) triggered thermonuclear fusion in its core. This is called a Type 1a Supernova. Matter flees the scene at about 3% light-speed, so it takes some doing to slow it down and incorporate solid fragments in a planet!
In the universe of Star Wars, Kyber Crystals are more normally employed as force conduits than weapons fuel. That's how lightsabers work -- they guide power from what's basically a multi-megawatt-hour battery into a blade field. It's also a truism that only a living thing can wield a lightsaber, because Kyber crystals only respond to living users.