Wells are a common motif in Warcraft. The Well of Eternity transformed the Dark Trolls and Yaungol into the Night Elves and Tauren, respectively, and while that Well was destroyed ten thousand years ago, its waters allowed the creation of other incredibly powerful wells, and its remains, the Maelstrom, are still an important part of Azeroth's landscape.
Not only that, but the Night Elves use sacred Moonwells that empower them with some sort of mix of arcane and holy magic.
So it should perhaps not be so surprising that Suramar City has a magical well at its heart that drives its society.
Suramar is not some unknown quantity invented for the sake of the Legion expansion. We've known for years that Illidan and Malfurion were born there (though that's a little like saying I grew up in Boston - technically, the Stormrage brothers and I grew up in the suburbs) and that it was one of the key cities in the ancient Night Elf empire (something I hadn't quite grasped is that Azshara the zone is actually the remnant of Zin-Azshari, which was the capital of the empire.)
Actually, Suramar was described as being just across the Well of Eternity from Zin-Azshari, which does leave some oddities in the game lore. The Well we saw in the Well of Eternity dungeon cannot possibly be large enough - on the maps of old Kalimdor, the Well was the size of a fairly large in-land sea, and we sure as hell couldn't see Suramar from Azshara's palace in that dungeon.
The other implication is that, rather than most of Old Kalimdor sinking beneath the waves, instead it really does appear that the continents and islands moved very quickly away from each other. The Broken Isles are much closer to the Eastern Kingdoms and Northrend than they are to the continent we now call Kalimdor.
If we accept that you could see Suramar from Zin-Azshari, that would imply that the zone of Azshara and the Broken Isles were once right next to each other, huddled around what is now the Maelstrom.
(Also, I assumed that Nazj'atar was built out of the sunken ruins of Zin-Azshari. Granted, maybe in the continental shift during the Sundering the city was kind of strewn out over a long span, with part of it in modern-day Azshara and part under the ocean.)
Setting this issue aside, let's talk about the Nightwell.
If Suramar, like Zin-Azshari, was really right on the Well of Eternity, it actually seems like the Nightwell would be very closely related to it.
Before Malfurion could detonate the Well and enact the Sundering, Illidan collected seven vials of water from the Well of Eternity. He gave one of these to Dath'remar Sunstrider, who brought it to the Eastern Kingdoms and used it to create the Sunwell on the Isle of Quel'danas. This font of arcane magic fed the people who would become the High Elves for ten thousand years, until the Sunwell was corrupted by Arthas in order to resurrect Kel'thuzad as a Lich. Later, Velen used the spark of the Naaru M'uru to reignite it, now as a font of both Holy and Arcane magic, allowing the Blood Elves to be have their magical addiction sated in a more wholesome manner.
Illidan used another vial to create a well at the top of Mount Hyjal, and in order to contain the magic there (lest it cause a second Sundering,) Malfurion, the Ancients, and the Bronze, Green, and Red dragonflights planted Nordrassil over it, allowing the World Tree to soak in the waters and stabilize it.
Two of the other vials were given to Vashj and Kael'thas much later (players used to have to gather these as part of the attunement quest to get to Black Temple, or maybe the Hyjal raid - I wasn't a raider back then so the only attunement I did was for Karazhan.)
So one might be tempted to think that the Nightwell was created with another one of these vials.
But this doesn't quite add up. The Sundering marked the end of the War of the Ancients, and it was only right before that point that Illidan gathered his vials. Suramar locked itself away before that point. Had the war been won already at that point, it's unlikely that Elisande and her followers would have made such a drastic move.
So we can probably conclude that the Well of Eternity and the Nightwell coexisted for some period of time.
The Nightwell is clearly not as powerful as the Well of Eternity - even the World Tree on Mount Hyjal is not as potent as source of power. But we know where these other wells come from - Illidan, basically.
I suppose it's possible that Illidan might have created the Nightwell as well. He was the leader of the Moonguard, whose headquarters are right outside Suramar City, and given his fascination with the power of the arcane, I wouldn't put it past him to have been experimenting with creating other Wells before the War of the Ancients.
In all honesty, that's probably the easiest explanation - Illidan was from Suramar and so it would make sense for him to want to help out his hometown by giving them a font of incredible power.
But let's consider different possibilities:
The Vale of Eternal Blossoms in Pandaria has been compared with Un'goro Crater and Sholazar Basin as a kind of Titan petri dish for experimenting with life. The Jinyu, for example, are actually Murlocs who underwent a similar transformation that the Dark Trolls and Yaungol went through, only instead of the Well of Eternity, they were transformed by the waters of the Vale. I believe pretty strongly that the Pandaren are in the same category, probably descended from Furbolgs who were empowered by the waters of the Vale.
But the waters of the Vale are something very different from the Well of Eternity.
In Chronicle, we find out that the Well of Eternity is actually a gaping wound in the nascent Titan Azeroth. As the Titanforged were warring against the Black Empire of the Old Gods, Aman'thul grew so worried for his creations that he physically reached down and tore the Old God Y'Shaarj out of Azeroth's surface. This did kill the Old God, but it damaged Azeroth so much that the Titans concluded they could not do the same with the remaining three Old Gods.
As Titans are beings of Arcane magic, the blood of Azeroth was an incredibly potent magical water.
Later, Sargeras would war against the rest of the Pantheon over their refusal to let him destroy Azeroth (he believed it was the only way to spare the universe from an Old-God-corrupted Titan.) Sargeras killed his fellow Titans, but not before they could send their spirits and memories to live on in the Keepers of Azeroth. Each Titan sent their essence into one or two keepers, and one of the Keepers to receive the spirit of Aman'thul was Ra-Den. Unlike the other Keepers, who were unable to make sense of the strange images and power with which they had been imbued, Ra-Den understood that their gods had been slain. Unable to bear the weight of that knowledge, he extracted Aman'thul's power from himself and poured it into the Vale of Eternal Blossoms, creating the magical waters there.
This all happened well before the War of the Ancients.
Could it be, then, that the Nightwell is not actually related to the Well of Eternity, but is instead the essence of a different Titan?
We don't know of any other Keepers realizing the implications of the Titans' final gift (Ra-Den didnt' tell anyone and instead went and sulked in Mogu'shan Vaults for the next several thousand years, until Lei Shen showed up and stole his heart - good thing a Keeper can live without a heart,) so it seems unlikely that the Nightwell would be created by some Keeper extracting the power of whatever Titan had empowered them.
However, recently, I've speculated a bit about the nature of Elune, and this could tie into what the Nightwell is.
My potential theory is that Elune is actually a Titan who pre-dates Aman'thul and never joined the Pantheon. In this theory, Elune is in a somewhat literal sense the mother of Azeroth. She sacrificed a great deal of her own power in order to make Azeroth the most powerful Titan in existence. She diminished in size after doing so, becoming one of Azeroth's moons.
Elune is associated with the Nighttime - which makes sense, as we do the same for our real moon even though technically the moon is just as often on the "day" side of the planet as it is on the night side (more or less.)
So what if the Nightwell is not Azeroth's blood, but in fact Elune's? Perhaps it was actually created not as a source out of which to extract power from Azeroth, but rather was meant to feed power into Azeroth?
Consider this - the Burning Legion's goal is to kill Azeroth's world-soul. Even though the planet is probably billions of years old, the Titan within is still essentially a fetus. If the Nightwell is effectively Azeroth's umbilical cord (which the elves of Suramar have been able to tap into and draw off some relatively insignificant portion of the power to sustain themselves) then if the Legion had control of it, they could pump deadly Fel magic directly into the World-Soul itself.
The Legion wants the Nightwell - has the Nightwell, actually - and is highly invested in keeping it. Perhaps this is the reason why they care so much about it.