Ghost Matter is a hazardous material found throughout the Outer Wilds' Solar System. While invisible to the naked eye, it can be detected via the silver crystals that adhere to nearby surfaces, or captured on camera by the player's Little Scout. When photographed, it appears as a ghostly blue-green aura in the air around certain Ghost Matter crystals. Interestingly, it is the only matter in the game that photographs in colour, although this is likely just a gameplay convenience, rather than a property of the matter itself.
It is extremely dangerous, and will kill anyone who stands within it for more than a couple of seconds, or severely injure players that pass through it at speed. However, it doesn't universally appear wherever there are Ghost Matter crystals, and some patches of crystal can be crossed safely - one can even stand directly next to the Ruptured Core without harm. Firing the Little Scout through patches of crystal, or taking photographs with the scout's camera can inform the player as to whether a path is safe to cross or not.
History
CAUTION: SPOILERS
Ghost Matter appears to have been brought to the system by the comet known as 'The Interloper'. Text logs indicate that the Nomai detected the comet's presence some time around the failure of the Sun Station project. Upon investigation, the Nomai explorers Poke and Pye found a way below the surface of the comet and discovered within it an incredibly dense, pressurised core of hazardous 'exotic material' - the crystal that the Hearthians know as Ghost Matter. Their tests indicated that the core was at risk of rupturing and the resulting explosion could wipe out all life in the solar system, but before they could warn anyone of the danger, the core detonated, killing them instantly. This event put an end to all Nomai life within the solar system, leaving behind only the remnants of their civilisation.
Notes
It is known from Nomai text logs that the primordial Hearthians existed in the volcanic waters beneath the surface of Timber Hearth at this time. It can then be inferred that they were shielded from the blast, and survived to evolve into the species we see in-game.
The crystals that accompany Ghost Matter appear to be shards of the Ruptured Core. Given that they aren't necessarily dangerous on their own, it's possible that the Ghost Matter itself is some kind of gas or vapour that was encased within the core, or radiation emitted from the crystals until they become inert. It's uncertain how the core came to be pressurised - whether it emitted the matter and pressurised itself, or whether it was pressurised intentionally, but according to in-game text logs, it presented no immediate danger before it exploded. It is possible, although there is no definitive indication in-game, that the core may be a weapon.