I'm pretty sure that by this point in time, everyone knows the basic gist of what Galaxia is: a sword. Meta Knight's sword, specifically.
Here's the thing though... despite at first not thinking much of it, the more I look into this, the stranger it gets, and I'm not about to keep the bizarre amount of information I've found on this specific topic to myself. Here we go...
The first time we saw Galaxia was in (the non-canon) Kirby Right Back at Ya! (though that's pretty common knowledge). In it, Galaxia was a "sacred" (or "holy", depending on how you translate it) sword forged by an ancient civilization (wait a second...), then to be stolen by NME and recovered by Meta Knight on his infamous mission with his (now deceased) friend Garlude. It is later explained that only those "worthy" can wield it without perishing, and though it is never explained what makes one "worthy", we've only ever seen Meta Knight and Kirby do it in the anime. It's partially implied that Garlude's daughter Sirica can also use it to an extent (though not completely?) but this is never explained and is probably not that important anyhow, so I'll skim over it for now.
The next time we get substantial Galaxia information is in Kirby and the Amazing Mirror, in which Meta Knight once again lets Kirby borrow his sword. Interestingly, it's not called "Galaxia", but rather "Master Sword". It looks a bit different too, so we can't be completely sure that it's the same one, but we can't assume it isn't either.
The thing that really caught my attention was the prefix "Master". In case you hadn't already caught on, this name (and the appearance of the sword, for that matter) is eerily reminiscent of the Master Crown, and it gets even stranger when you look at Magolor's (the wielder of the Master Crown) Ultra Swords in his Soul fight:
Oh.
This is the part where things start to fall into place. Does this mean that Galaxia is a Sword equivalent of sorts to the Master Crown? Does this mean that it too is controlled by Dark Matter? Does this mean that it could also potentially ruin Meta Knight's body at will and give him that oddly unsettling eyeball-mouth look? Does this mean that (dare I say it?) Galaxia ties back to the Ancients?
Wait... let's return to that Dark Matter thought for a moment. Void Termina also uses Ultra Swords, so do they change appearance in the Soul Melter version of the fight?
They're Galaxia-looking again! Void Termina also uses a mimic of the Master Crown in its battle, so that solidifies the theory that both artifacts might be connected somehow, perhaps through the Ancients or the Heroes of Yore (it would tie back to KRBAY's mentions of "worthiness" and "ancient civilizations" after all).
Great! It seems we have a really solid theory as to the origin of Galaxia, and all of our evidence is fitting together quite nicely! I sure do hope nothing incredibly confusing shows up out of nowhere and blows the entirety of these "clues" out of the water!
And so:
Apparently, Morpho Knight's sword briefly gains this appearance during one of its attacks. How does this tie into Galaxia and Meta Knight, you ask?
...I have no clue. It's Morpho Knight, what did you expect?
Conclusion: Oh no.