They are some form of super-deities, or perhaps a personification of some multiversal axiom about true evil. They are never described in character/deity terms, and in fact have imprisoned some impressively powerful beings, including a couple deities from other D&D game worlds. (Vecna, specifically, being the most noted, but there was another.)
The Dark Powers are noted only by what they do, and that is, they reward evil acts with more power, but at a price of less freedom. Sufficiently corrupt individuals find a chunk of the demiplane altered to become their own personal hell... LOADS of power, but trapped forever there, and unable to get whatever it is they truly desired in life.
The Dark Powers also search the multiverse (or at least the Prime Material Plane) for certain "worthy" individuals, and set the Mists upon them. If they don't flee the Mists, anyone near the victim also is transported. The area is removed from where it was, and attached somewhere in the demiplane.
It is worth noting that they control the demiplane, and can affect all within it. They can not, however, prevent Vecna from granting spells nor communing with his clerics, but they can prevent him from making personal appearances. They have moved regions about, deleted regions, and made and deleted borders on an apparent whim.
The Dark Powers do not use manifestation forms, do not reveal themselves if they use mortal forms, do not grant spells, are not subject to commune spells. Even calling them entities or an entity is a stretch.
Source Note: It is worth noting that the nature of the Mists grabbing parts of the Prime Plane was the focus of one of the TSR Retail Play modules for AD&D 2E; in that same module, PC's who do not flee the Mists wind up in Ravenloft as well. The demi-plane does not provide inhabitants; it captures them with the evil being.
In the 3E materials from S&S, it's noted that at least one domain dark-lord was originally from the Demi-plane. Another was in the demi-plane already when the Dark Powers noticed them.
In the case of demons, the monster description (MM p. 50) argues against the reverse of falling that the angels are susceptible to.
Possessing no compassion, empathy, or mercy, they exist only to destroy.
Angel: pride can lead to a mistake that leads to a fall. (MM p. 15)
Demon: opposite of angel ~ the opposite of pride is humility.
Humility doesn't fit the profile of lacking empathy, mercy, and compassion. From that starting point, the DM needs to establish a motive that outweighs this fundamental characteristic of a demon. Something, some experience, someone, or some event induces a demon to act in an other than selfish and destructive manner.
The DM then must resolve how a creature spawned as an extension of the Abyss (MM p. 50, Spawn of Chaos) breaks free of that influence sufficiently to change its nature. In the case of demons formed from mortal souls (since in 5e souls exist) the memory of being something other than a demon could provide the leverage needed to initiate change. In that case, the specific follow-on effects will vary as with the motive for change.
Two simple and opposed potential outcomes:
- The demon leaves the Abyss forever, never to return
The demon enlists allies to return to the abyss and avenge ---
something.
(And many points between). Without a story hook on the why of a demon's change, the what of the aftermath of the change is too varied to nail down.
MM p. 7 (RAW boils down to "You can if you want to.")
"Feel free to depart from it and change a monster's alignment to suit
the needs of your campaign. If you want a good-aligned green dragon,
or an evil storm giant, there's nothing stopping you.
The only thing stopping the DM is the crafting of an in-world reason that fits the larger narrative of the campaign and the story. The only constraint is the imagination of the DM, not a rule.
What makes for a good change is a decision to create the exception to the general rule of the MM default description for demons - the general case is that a demon isn't motivated to change. Establishing motivation is step zero to this change occurring in, or fitting the narrative of, a campaign.
If lore extends beyond 5e, something from 2e Planescape or FR novels may offer a concrete example.
There were a few risen fiends in 2e Planescape - Fall-From-Grace the succubus, and Morte the floating skull whose provenance is something of a spoiler ~ {Thank you @nick012000}
Best Answer
Power derived from souls is required
The Fiendish Codex 2 from 3.5e includes a lot of information regarding promotions, including on page 11:
Further, it is also mentioned on page 12 that this also affects demotions:
Page 9 of the same source contains details on the process of extracting the required energy from the souls:
"Local lord" in this passage refers to the Lords of the Nine Hells which are also mentioned in the 5e Monster Manual.
D&D 5e
Some references related to promotion can be found in MToF. The Three Paths to Power1 section in particular includes some information on how the different devils are chosen for promotion, which can be considered a form of constraint or limitation for promotions:
The three paths are Souls (receiving credit for collecting mortal souls), Glory (receiving credit for slain foes) and Treachery (replacing a superior by getting them killed)
The Monster Manual entry on devils, under Infernal Hierarchy1 also refers to a constraint on promoting only certain devils (and not just any lower-ranked one):
Unfortunately, I was unable to find any information from 5e specifically detailing an actual resource being consumed for promotion, as the references above from 3.5e. I searched the Monster Manual and the Blood War section on MToF.
Note that in the case of demons, the Monster Manual does mention that demon lords expend "considerable magical power" to promote lesser demons but no such specific language is used for devils.
1. As suggested by illustro