With most fictional superpowers, there is at least a plausible, if not realistic, mechanism of action: Superman is an alien with physical traits only superficially similar to humans, and his talents can be hand-waved by biology, Spiderman was bitten by a radioactive spider, which produced mutations that modified his body to give him his powers, and so on.
We can also attribute speculative mechanisms to superpowers in real life, though: if we saw someone with the attributes of Spiderman, we could speculate about what mechanisms allowed them to exhibit the powers they do: what could the webbing be made out of? What biological process could produce it in humans? And so on. In some cases, such speculation may reveal inherent contradictions, due perhaps to unphysicality (what if someone moved faster than light?). But we really have to stretch to reach this point, and in many cases we can outline realistic — or not demonstrably unrealistic, e.g. time-travel related — mechanisms for seemingly implausible powers.
Recently, I played a game in which one of the characters had, as their distinguishing power, a supernatural luck. This luck, as most depictions of supernatural luck, is far beyond mere serendipity: it can be replicated arbitrarily without any action on the part of the lucky person. A supernaturally lucky person will, if their life depends on it, flip heads ten times in a row without any tricks; if you shoot them, you can expect your gun to jam; if you push them off a building, they will land on a window cleaner's platform two stories below. (You can call this "plot armor", if "luck" is disagreeable).
With the above in mind, what are the possible mechanisms by which a supernatural luck could manifest in real life? I can identify two families of mechanisms, corresponding to two ways in which one can reason about causality: forward-causal mechanisms, and backward-causal mechanisms. I will elaborate on each. Throughout, I will make the following assumption: luck "acts" in order to achieve a goal G, which I'll take for the sake of example to be the preservation of the luck-bearer's health (though it could really be anything).
In this family of mechanisms, there is some force which directly manipulates physical reality so as to achieve G. For instance, a guardian angel.
If someone points a gun at you and pulls the trigger, your luck will, perhaps, slightly move the primer of the bullet such that it does not detonate when struck by the firing pin, causing a misfire. If you're pushed off a building, luck might slightly adjust your trajectory so you, instead of dying, merely break both your legs.
The ways in which types of luck in this family can vary are as follows:
What luck can directly manipulate, and how it can manipulate it.
Can it make people prone to thinking certain thoughts? make small objects move? alter the execution of computer programs? create, transmute, or destroy matter (for instance, altering the molarity of a solution of hydrofluoric acid splashed in your face)?
How intelligent luck is.
Consider the gun example: from the outside, it might seem that luck causes the gun to misfire, and that's that, but really there must be a reason why the gun misfired, detectable by appealing to the causal mechanism by which the gun works. In order to cause a misfire, luck would somehow have to "know" this causal mechanism — namely, that the firing pin strikes the primer, which detonates the propellant and thereby propels the bullet. It would then have to "deduce" a way in which it could throw a wrench in this mechanism, (1) deducing that preventing the firing pin from striking the primer would cause a misfire, (2) determining that it could prevent this by moving the primer relative to the bullet, and (3) figuring out how much to move the primer in order to cause this to happen.
We can think of this in another way: the vast, vast majority of minor alterations luck could make to reality would do absolutely nothing to achieve goal G — in fact, many of them would achieve the opposite. So luck has to sort through all of these options in order to find an efficacious one. It can do this "more intelligently", picking those alterations which square with the causal structure we ascribe to the world around us, or less intelligently, picking alterations independent of this causal structure. A less intelligent variant of luck would look more inexplicable: the gun jams, but upon inspection it's not immediately clear why.
How far luck sees ahead.
For luck to work at all, it must be able to judge the impact of any given alteration it looks at on the goal G. But, how far ahead does it look? Namely, how far back can luck deduce that G is about to be compromised — that it has to do something? Does it do so when there is a clear and immediate threat, for instance someone pointing a gun at you, or does it see into the future, somehow inferring that, unless it does something, G will be compromised in two hours/days/years? Luck that looks sufficiently far ahead may, for instance, simply mess with the shooter's car as he's driving to you in order to cause a fatal crash. A luck that acts in this way likely wouldn't even be noticeable, and if it were, it would look like a vast, subtle, and all-knowing conspiracy.
Another way to set this parameter is by appealing to human reason: luck would only notice those threats that a human would notice, at the same time that a human would notice them. Perhaps it only acts on those things the bearer of the luck notices themselves; in the same way, perhaps it only uses what knowledge the human themselves has (though it would be very weak in this case).
The usual kind of supernatural luck encountered in fiction can only notice what humans are capable of noticing, but is intelligent enough to know how to make things like gun jams happen even when the bearer of the luck is not. It is capable of manipulating physical matter and electronic information, but seems to stay away from manipulating thoughts or creating or destroying matter.
In this family of mechanisms, we have a notion of different timelines — nondeterminism or whatever means that, for every state and progression of reality, there are (hypothetical) alternate timelines where reality progresses in a slightly different way. Luck does not alter the world through any physical force, instead pruning timelines where G is going to be compromised, leaving only those timelines where it is preserved.
Timelines in which certain events happen are less or more frequent in the 'space' of all timelines according to the tendency of those events to happen — if G is setting a particular person on fire, timelines where they spontaneously combust are far rarer than those in which they have an accident while operating a lighter or kitchen stove, or in which an electrical malfunction burns their house down with them inside; a weak luck, having difficulty pruning timelines, would therefore be far more likely to select a timeline where the house burns down rather than one where the person spontaneously combusts. We may call backward-causal forms of luck more or less powerful depending on their ability to prune timelines.
To the perspective of us, who can only inhabit one timeline, it would seem as though a series of accidents prevented G from being compromised, but, really, luck acts to make sure that it never could have been compromised.
If someone points a gun at you and pulls the trigger, the gun will jam not because some supernatural force acts on it, but because the shooter loaded the gun improperly, the bullet was defective, etc. — some 'natural' reason. If the shooter is an expert using only the best ammunition, so that timelines where they fail to fire are extremely rare, enough so that luck isn't powerful enough to find one, luck may instead find a timeline where the bullet doesn't hit any internal organs, and in which you manage to escape.
The ways in which kinds of luck in this family can vary are largely different from those of forward-causal luck: in particular, this kind of luck needs no intelligence, only to be able to gauge whether G is compromised; it does not manipulate things either. The two main ways in which backward-causal forms of luck can vary are:
How it prunes timelines.
It can either do it in advance, determining that G is going to be compromised in the future, and manipulating whatever nondeterministic phenomenon makes this luck possible in order to move to a timeline in which G is not compromised, or ad hoc, noticing that G has just been or will immediately be compromised, and shifting to a nearby timeline in which it hasn't been.