Outside, looking in
Hunger of Hadar:
A 20-foot-radius sphere of blackness and bitter cold appears, centered on a point with range and lasting for the duration...No light, magical or otherwise, can illuminate the area, and creatures fully within the area are blinded.
Nowhere does the spell explicitly say that it produces 'darkness'. Rather, it produces "blackness and bitter cold". Within the rules, 'cold' is a kind of damage, and the spell later quantifies this as 2d6 per turn. But 'blackness' has no game description, although its natural use in English suggests that it may be related to darkness. Thus, as NautArch says in their answer, we need to define blackness.
The spell also says that no light can illuminate the area, and that creatures within it are blinded. Is this the within-game definition of blackness? Possibly. We can't be sure, but ultimately it doesn't matter - because if 'no light can illuminate and blindness within it' is the definition of blackness, then we know how to apply it. And if this is not the definition of blackness, we still have to apply 'no illumination, and blindness' as a spell effect, and since we don't know what blackness means we cannot apply it anyway.
The fact that no light can illuminate the area is related to the lighting conditions defined by the rules (and cited in full by findusl's answer). In brief:
The presence or absence of light creates three categories of illumination:
When an area is fully illuminated, it is in "bright light".
An area between bright light and darkness is "dimly lit", as is an area that is illuminated by a particularly weak source of light.
An area that is insufficiently illuminated, or not illuminated at all, is in darkness.
Thus, although the spell description does not explicitly say that the sphere is an area of darkness, by telling us that it cannot be illuminated we know that it fits the game definition of darkness.
For the purposes of who can see in this darkness, we might need to know whether or not it is magical. As the Sage Advice Compendium tells us (v. 2.7 p.21), since the blackness is produced by a spell and powered by spell slots, this would be magical darkness. However, Sage Advice (v. 2.7, p.3) also tells us:
Magical darkness blocks darkvision only if the rules text for a particular instance of darkness says it does. For example, the darkness spell specifies that it produces a magical darkness that obstructs darkvision. That obstruction is a feature of the spell, not of magical darkness in general.
We can conclude that the 'blackness' produced by the spell is magical darkness, but it is magical darkness of the kind which does not block darkvision.
Thus, from the outside looking in, the blackness of the spell would block the vision of only those who cannot normally see in darkness. Those with Darkvision are allowed to treat the magical darkness as dim light, and those with Devil's Sight can "see normally" (that is, with no penalties on Perception checks, and the ability to see colors).
As per the spell description, creatures actually within the blackness are Blinded, meaning they "can’t see and automatically [fail] any ability check that requires sight." This will supersede both Darkvision and Devil's Sight, since using these requires that the creature to be able to see. The only creatures that will be able to see out of the blackness are those who rely on a sense other than vision to see (such as those with Blindsight).