When I ask "What does the color of the darksaber mean?", I am referring to its kyber crystal color. In the Disney canon, kyber crystals change color depending on the wielder's place in the Force. Dark Side wielders' crystals turn red because they "bleed," and Ahsoka Tano's crystals turn white due to her lack of affiliation with any side (although she was definitely more of a Jedi that time). The first Mandalorian Jedi, Tarre Vizsla, created the Darksaber. What does this say about his affiliation with the Force?
First off: kyber crystals only change colour as they bond with (or in the case of dark side users: dominated by) the individual constructing the lightsaber. At that point the colour is "fixed" and doesn't change based on who happens to be wielding it at any given time. The only way the colour can change is if the crystal is bonded with and built into a new hilt.
Secondly: Aside from "red=dominated", the precise meaning (if any) behind the colours of bonded crystal is unknown, even in-universe. This appears to be by design and meant to be yet another mystery of the Force.
The idea that Ahsoka's blades are white as a direct result of her being neither Jedi nor Sith is pure speculation. Likewise, until we hear otherwise, any reasoning behind the darksaber's blade being black would be equally speculative.
That said, the idea that it's because it's tied to the dark side seems directly at odds with established canon. Kybers don't turn red because their users are dark side users (not directly anyway) they turn red because the nature of a dark side user precludes them from being able to form a sympathetic bond. They only know how to dominate and turning red is how kybers react to an imposed, unnatural bond. As such, in these instances it's not reflecting the individual as it does in a natural bond, but the method by which it was bonded. Hence: always red. Therefore anything other than red should be a natural bond or the result of some other unknown factor that's yet to be addressed.
The history behind the darksaber appears to be something they only started to really think about in any detail when it cropped up again in 'Rebels'. Based on what's been said it seems they only thought about it in broad strokes for it's appearance in TCW; that it was an old relic pilfered from the Jedi Temple by Mandalorians and used as a symbol of power for the warrior clans.
The real reason for its colour is of course because the filmmakers wanted something that looked unique. After Lucas nixed the idea that a vibro-blade could ever block a lightsaber they went though several iterations of what an unusual lightsaber might look like--including a yellow blade--before settling on the black blade.
Indeed, it's worth keeping in mind the real-world history of why these different blade colours have been used over the years. Originally they were all intended to be white blades as per Ralph McQuarrie's concept art (and I believe briefly they were all going to be red, but I may be mis-remembering.) This was changed to blue and red to make it visually easier to distinguish between Vader & Ben's blades in some of the faster moving close and medium shots. Indeed, the initial intent was to do the lightsaber effect entirely in-camera with highly reflective material and a light behind camera, but when that method proved impractical and problematic on-set, they ended up rotoscoping them all in post anyway.
Luke's green blade in RotJ came about simply because they were shooting with a blue sky in the background during the sarlacc action sequence and it made the blue blade difficult to see. Mace Windu's blade was purple simply because Sam Jackson asked for it and similarly Ahsoka's new blades were white because Dave Filloni liked how it looked. Not sure if the Temple Guard's having yellow/gold blades was ever addressed, but I imagine it was probably something to do with the distinct yet uniform nature of their look that separates them for other Jedi, and possibly partly to re-enforce the notion that they're antiques from an earlier era.
SIDE NOTE: This is just me speculating but I think it's possible that rather than somehow emitting "black light" I think the darksaber's blade acts more like the event horizon of a black hole. That somehow the energy current is bending light around the blade instead of up and down it. This may also account for the white halo being analogous to the lensing effect typical of such phenomena and the blade-like solid looking shape instead of the usual straight glowing beam. In which case the kyber inside may actually be white, or some other colour but the unique design of the hilt and the blade emitter is producing this unusual effect. If nothing else, Mandalorians are known for being inventive when it comes to their weaponry!
What's really interesting is that the color of the Darksaber didn't change with different owners. When Maul, whose lightsaber is red, took the Darksaber from Pre Vizsla (note: I have no idea what I'm talking about or what this is from. I got it from Wookieepedia [here], so if it is wrong, don't hesitate to tell me.) Anyway, when Maul gained control of the Darksaber, it did not change to red. Consider this quote from Ashoka, which I found here:
“I’ve never seen white ones before,” Bail mused.
“They used to be red,” Ahsoka said. “When the creature had them, they were red. But I heard them before I ever saw him on Raada, and knew that they were meant for me.”
“You changed their nature?” he asked.
“I restored them,” Ahsoka replied. “I freed them. The red crystals were corrupted by the dark side when those who wielded them bent them to their will. They call it making the crystal bleed. That’s why the blade is red.”
Maul certainly would wield any saber, light or dark, to his will and corrupt it. The fact that it didn't change color could mean two things:
One: The Darksaber's color means the same thing as the red color.
According to Wookieepedia,
Black was generally associated with night and evil, especially the Sith. The colour "Sith black" was considered a symbol of their ancient dread.
Two: The Darksaber is different from a normal lightsaber.
I can't find anything that confirms or denies either of these theories.
I would guess that the darksaber is black b/c of a process of lightsaber construction that differs somehow from the usual construction. But this is obviously purely speculative. An alternate possibility I find plausible is that something about his Mandelorian culture/upbringing made the way he was attuned to the force influence the kyber in such a way as to produce that unusual hue.
Additionally, I'll add that we have seen in Canon that the process of making a Kyber bleed seems to require that a sith or other dark user concentrates all of their negative emotions and pushes them into the crystal, bending it from its natural light-sided state into a dark one, thus giving the red bleeding effect. It seems to take a good deal of effort. (This information comes form one of the canon comics where Vader is sent by the Emperor to turn his lightsaber to the dark side/make his kyber bleed for him) If we take this fact and assume a similar method is required for tuning a kyber to a Jedi's force ability, (something we can sort of see in that one deleted scene where Luke Skywalker is building his green lightsaber) then we can assume changing the colour of a kyber is always a labour intensive event, involving much concentration. (call this an "educated guess," at least) To that end, it just makes sense that the darksaber's colour has never changed since few, if any force-sensitives have wielded it since it's creation.
Lastly, I just want to mention (as was kind of touched on, I think) Ahsoka Tano's white lightsabers are a result of taking a dark-user's red/bleeding lightsabers and turning them back to the light side. B/c they have been damaged by the bleeding process, the only colour they can be now besides red is white.
To me, white lightsabers just scream "I'm a badass dark-user hunter" lol. But obviously the ways one could acquire a red lightsaber to be turned white are many, not just b/c you "hunt" dark-siders.
If we go on the assumption that the reason Ahsoka's sabers were white was because she wasn’t a traditional Jedi, but instead because she was (best described as) a grey Jedi, she still held affiliations to the light, making her a “light grey Jedi” but opened herself up to things like vengeance and an affection, then since Tarre Vizla was a Mandalorian, whose culture is much darker than the average humans, his saber attuned to be black due to him being more of a “dark grey Jedi” than a traditional Jedi, he still honoured his heritage which would not be the Jedi way, by donning Mandalorian Armour, and the Mandalorian way is that of bloodshed, murder and war. The edge of the blade being white gives me the impression he wasn’t a fully dark Jedi, and the reason his crystal isn’t red is because he didn’t force it to submit to him and become a sith crystal, the crystal bonded to his darker nature naturally, likely during his trials. As for why it’s remained black, that’s likely something to do with the fact nobody has removed the crystal to force it to submit, along with the fact that it’s unique in being a naturally dark aligned crystal.
The reason the darksaber is black is because it did not use a regular Kyber crystal. Now I do not know what kind of Kyber crystal, if any, it uses but the darksaber is actually some kind of black hole contained in the saber shape.
Also Ahsoka's white lightsabers are actually from two restored bled Kyber crystals that when she restored turned white as they were both not attuned to her as Kyber crystals are when they change color.