Superdeterminism is a response to Bell's Theorem. It is one of two ways that a certain assumption required to prove Bell's Theorem might fail.
The assumption in question is most commonly called "Statistical Independence". More accurately, it would be called "Statistical Independence between the past hidden variables $\lambda$ and the future settings $(a,b)$", but that's a bit of a mouthful. In mathematical terms, this assumption would look like $$Prob(\lambda)=Prob(\lambda|a,b).$$
The idea here is that one can try to model entanglement by assigning a probability distribution $Prob(\lambda)$ to the shared hidden variables of the two particles, back when they are first entangled. The above equation is the assumption that any reasonable model must assign those probabilities for $\lambda$ independently of the eventual measurement settings $(a,b)$ for that run of the experiment. It seems like a reasonable assumption, but if we break it, the central argument of Bell's Theorem doesn't go through. (If this assumption failed, then one really could explain entanglement experiments in terms of localized hidden variables.)
Superdeterminism is the idea that one can violate the above equation, explaining correlations between $\lambda$ and $(a,b)$ in terms of past common causes. Specifically, there could be some distant past set of hidden variables $\Lambda$ which would serve to correlate $(\lambda,a,b)$. That argument makes sense to the point where you consider $a,b$ to be some microscopic details in the measurement device, perhaps why you're asking about hidden variables in the measurement devices themselves. Certainly it would be unreasonable to insist that a model had no correlations between those details.
But ${a,b}$ aren't microscopic details. They are macroscopic settings, chosen in some manner. They're the values written down in the lab book when calculating the entanglement correlations. As Bell himself put it, they could be chosen by the Swiss Lottery Machine. So any superdeterministic account can't merely correlate hidden details. They have to correlate the output of the Lottery Machine in Alice's lab, with the output of the Lottery Machine in Bob's lab, and both of those in turn need to be reproducibly correlated with the original hidden variables back where the entangled particles were generated. If you can't find an account in the literature explaining what those hidden variables might be, it's probably because there's no conceivable set of hidden variables which could account for every way that the settings $(a,b)$ might be chosen.
The other way to break Statistical Independence is having a model which is "Future-Input Dependent", or "Retrocausal", at a hidden level. Instead of a common-cause explanation of the correlations, now the explanation is a direct cause, from $a$ to $\lambda$ and also from $b$ to $\lambda$. (This assumes one is using Pearl-style interventionist causation, where the external intervention/setting is always the "cause" by definition. If you don't take this view of causation, such models are hard to wrap your head around, but can still be analyzed in terms of the input-output structure of the underlying model as described here.)
Some papers (and also the initial definition on Wikipedia) blur the distinction between retrocausal and superdeterministic models, calling them both "superdeterministic", but this seems misguided to me. Clearly there's an enormous conceptual difference between direct retrocausal influences from $(a,b)$ to $\lambda$ and a common-cause explanation of $(a,b,\lambda)$.
