The origins of Cresselia were never truly explored in the games, and there’s indeed very little we can say about this Legendary Pokémon. The Pokédex entry it was introduced with in Diamond and Pearl was the following:
When it flies, it releases shiny particles from its veil-like wings. It is said to represent the crescent moon.
This is a good adaptation from the original Japanese, but let’s give it a closer look:
飛行するときは ベールのような 羽から 光る 粒子を 出す。三日月の化身と 呼ばれている。
When flying, it emits glowing particles from its veil-like feathers. It is called the incarnation of the crescent moon.
It’s important to underline the use of 化身 [keshin]. The official localization rendered this as “represent”, but there are nuances that can be easily overlooked without considering the cultural context behind this choice of wording. The closer term you can translate it is “incarnation”. 化身 is used, in particular, to refer to the physical embodiments of Kami and other mystical beings — note that while the word 神 [kami] is often translated as “god”, this concept has actually a wider meaning and can refer to all kinds of spirits and supernatural entities worshipped in rituals.
Pokémon uses this term, for example, to describe the Incarnate Formes of Tornadus, Thundurus, Landorus, and Enamorus, as opposed to their “true” appearance in the Therian Formes. So, speaking strictly with the franchise own terms, the Pokédex is suggesting Cresselia to be the “Incarnate Forme” of a Kami called the Crescent Moon. Or, if you like it more, that the Crescent Moon is the “true” shape of Cresselia.
We know the Moon as a whole does hold special powers in the Pokémon universe. Its influence can be used to be reinvigorated with the move Moonlight [つきのひかり, Moonlight], or to channel a powerful energy attack through Moonblast [ムーンフォース, Moon Force]. As the mystical abilities this celestial body possess, it makes sense for people on Earth to consider the Moon as an entity to worship. And since it has its own incarnations, the divine status of the satellite is indeed grounded in reality.
Cresselia does not incarnate the whole Moon, but more specifically the Crescent Moon [三日月] — like even its original category みかづきポケモン [Crescent Moon Pokémon] underlines. By dictionary definition, this is “the Moon as it appears early in its first quarter or late in its last quarter, when only a small arc-shaped section of the visible portion is illuminated by the Sun”. Note that while localization occasionally renders the concept as “quarter moon”, no distinction is made in the original.
On nights around the quarter moon, the aurora from its tail extends and undulates beautifully.
As a matter of fact, both Cresselia peculiar moves references the Crescent Moon specifically: to Lunar Dance [みかづきのまい, Crescent Moon Dance], Legends: Arceus added to the movepool Lunar Blessing [みかづきのいのり, Crescent Moon Prayer], a “prayer” through which the incarnation can heal thanks to the blessing of its main body.
This also means lunar phases hold different and peculiar powers that are casted on the Earth, and as such they could have different incarnations representing different types of Kami. The Lunar Feathers the Pokémon is covered of are actually みかづきのはね [Crescent Moon Feathers]. As they are described as objects “said to possess the power to dispel nightmares”, the specific influence this being is able to casts upon the world is that of calming one’s dreams.
Those who sleep holding Cresselia’s feather are assured of joyful dreams. It is said to represent the crescent moon.
In other words, the Moon’s true nature seems to be directly tied with the Dream World. This will establish a recurring motif through the whole franchise: for instance, the Therian Formes of the Forces of Nature will be later revealed to have been originally discovered lingering into the Interdream Zone. As if in the Pokémon World the truest forms of Kami tend to be tied to the sleeping realm.
Although the word 化身 is never used in relation to Darkrai, its deep connection with Cresselia and the fact Pokédex descriptions ties it to another lunar phase leaves little doubt in the room: this is another incarnation of the Moon Kami.
It can lull people to sleep and make them dream. It is active during nights of the new moon.
Darkrai is the embodiment of the New Moon [新月], “the time at which the Moon is in conjunction with the Sun, when it is not visible from the Earth.” As it lurks people into nightmares, this Kami has opposing powers to the waking Crescent Moon; but with the Pokédex stating it means no harm, this lunar phase doesn’t seem to possess malevolent intent, and it rather spreads its influence on Earth as a mere consequence of its nature, and as a self-preservation mechanism towards those who consider its incarnation a fiend.
Folklore has it that on moonless nights, this Pokémon will make people see horrific nightmares.
To protect itself, it afflicts those around it with nightmares. However, it means no harm.
This is perfectly showed by Darkrai’s ability, Bad Dreams [ナイトメア, Nightmare]: regardless of its volition, the Pokémon will naturally drain lifeforce from those asleep nearby, consuming their dreams and turning them into nightmares. This isn’t to say the New Moon can’t fight when the situation requires it: the peculiar move Dark Void [ダークホール, Dark Hole] can purposefully put the opponent to sleep, making it descend “into a world of total darkness” according to the move description — something particularly fitting for the Pitch-Black Pokémon.
This black dimension seems to be one of nothingness, where consciousness goes blank and submerged thoughts devour you — to a point Masters compared it to the spiritless world Cyrus is seeking:
“If you sympathize with Darkrai and would like to spend time with it… you have to be prepared to enter a world of pure darkness.
If you can accept a world of nothingness, then you can truly understand Darkrai’s spirit. That’s what it means to be together with Darkrai.”
To any sane person, however, this is a true nightmare realm. In all likelihood, this isn’t a plane external to the Dream World, and more of an inner layer — opposed to the superficial Interdream Zone — where deepest fears can slip through the cracks of a weak mind. Darkrai relation to the sleeping world was further stressed out in the short “Pokémon: Pikachu, What’s This Key?” released with the 17th movie, where it is further affirmed the Pokémon has its own dreamy pocket dimension. This was also referenced in-game with an official Darkrai distribution with OT: “ ふしぎのくに [Wonderland].
This whole reconstruction naturally begs a question: what about the “Full Moon”? With the other phases having their own incarnations, you would expect the bright satellite to also be a Kami of some sorts. While it is true Lugia has been associated with the Moon by the developers, it seems to lack the connotation of embodying its “full” aspect specifically, and as Lunala is an invasive species we are in a lack of candidates. If it wasn’t for Cresselia itself.
In Pokémon Diamond, Pearl, and Platinum, we can catch the Lunar Duo in particular islands off the coasts of Sinnoh. While Darkrai’s home is coherently named Newmoon Island [新月島], its counterpart inhabits quite a peculiar place. Despite even the map notices a “crescent-shaped pond” lies inside its closed-off forest, the area is actually called Fullmoon Island [満月島]. How so?
Odds are, Cresselia and Darkrai are actually meant to represent the whole cycle. Other than lunar phases, the two Pokémon are clearly associated with the broader concepts of light and dark, and connecting this to the celestial motif we can depict a clearer picture. The Lunar Pokémon is the “bright” in the Moon, which starts to be more and more visible starting from the New Moon up to the Full Moon; the Pitch-Black Pokémon, on the other hand, is the “dark” on the satellite, growing more and more from the Full Moon to the New Moon — this is why its body is roughly shaped like a crescent too, only inverted compared to Cresselia.
What happened here, in simple words, is that Game Freak simplified the concepts of “waxing” and “waning”, mistakenly attributing the word “crescent” purely to the former — to play their advocate, the difference isn’t as evident in Japanese. Cresselia is meant to incarnate the light that grows up until the Full Moon, hence the name of the island it resides on. Darkrai opposes this light, blackening the surface until its total engulfment in darkness: the New Moon. At this point, the Lunar Pokémon starts to take over once again, and the cycle repeats.
On an ending note, we have to focus on a description Pokémon Legends: Arceus has brought to the table, as it could be a bit confusing. Cresselia’s Pokédex states:
Cresselia is reminiscent of the crescent moon. It leaves a brilliant line of light in its wake as it flies across the night sky. I daresay it resembles the heavenly maiden who created the Milky Way.
The last part is odd to say at least. Does this mean Cresselia created the Milky Way? Or that there’s a galaxy-generating maiden entity who resembles the Legendary Pokémon appearance? Not quite, if we look at Japanese wording.
眉月 想わせし ポケモン。 夜空を 飛翔の折 一筋の光跡 鮮明に残す。 まるで 天の川 産みし 天女なり。
A Pokémon reminiscent of the crescent moon. As it flies in the night sky, it leaves a clear trail of light. As a celestial maiden birthing the Milky Way.
Through the original text, it’s clear Laventon is speaking metaphorically: Cresselia leaves a bright trail in the night sky at its passage, giving the impression the Pokémon actually births the band of light we can see up in the celestial vault from which our galaxy got its name from.
Indeed, the Japanese from Milky Way is 天の川, which can be also read as “River of Heaven”. So, the trail Cresselia generates is compared to a river, which the Pokédex poetically equates to the entire galaxy.