See the Daimonion of Socrates (Wikipedia link). This is a first clear articulation of conscience, seperate from game-theory self-interest, or holding to divine laws. Biologically, I would describe conscience as exactly that, the experience of collective benefits of certain behaviours and values, as more important than personal benefit of eschewing them. That is, our eusociality, our ability to cooperate, feeling more valuable than self-interest.
I argue here that Socrates is paradigmatic in defining philosophy from other wisdom traditions: Weren't there any philosophers from Africa, America or the Middle East before Socrates? His 'martyrdom' for wisdom, his choice to give up his life and drink hemlock rather than recant his views which he described his conscience or daimonion as dictating, had a profound influence on Western thought exactly because he was saying, this behaviour of Socratic dialogue, and the challenge to 'piety' of the Euthyphro Dilemma, which I'd say is the core of what got him a death sentence, that these were values that could enable something about a collective holding to them, worth giving up his life for.
Plato took Socratic dialogue and the math-mysticism of Pythagoras to create his Academy, and so academia. Aristotle's Lyceum modelled the aspiration to universal education, and so universities. In this conscience, and a mutual interest in finding the truth, wins above rhetoric and sophism, over formal debate based on winning over an audience. Science requires a personal adherence to it's standards, not simply a wish for prestige by any means. We see this manifested in how scandalous scientific fraud is, to distort results like data dredging eg p-hacking, can disqualify someone from any credibility in their scientific work.
So, I would describe this as an articulation of morality, of the personal experience of the moral weight of actions, of when collective benefits are felt to outweigh any personal gain. This is key to any military, a soldier must be willing to die for their polity, and that is a core feeling, that defending a collective is worth sacrificing the personal, which enables civilisation, cities and polities. See Hume's "Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them", which highlights that felt motivations are fundamental, and reasoning can only come after.
Ethics however is not about the personal feelings, the inner conscience, but about persuading others how they should behave. This I argue fundamentally depends on intersubjective reasoning, here: Is the Categorical Imperative Simply Bad Math? :) That is, ethics must appeal to or educate the conscience.
Moral Foundations theory (Wikipedia link) is based on research showing there are core cultural universals, that seem to have evolved to support prosocial behaviour, eg a drive for fairness/justice. We can see this iterating from Ancient Greek myths about how bad absolute rulers eg Sisyphus, Minos, and Midus, could in some sense escape accountability in their lifetimes, but not beyond that; up to the Abrahamic idea that im this life, no one is above the law, which has enabled larger scale cooperation (at least, for now..).
There seem then to be core drives which evolved to let us cooperate, which we relate to conscience, morality, and the felt moral weight of actions. Then there is ethics, which aims to appeal to educate and refine the consistency of how we act on our moral feelings.
There is a failed assumption to intersubjectivity. There is a low but stable number of sociopaths and psychopaths across all societies. The gains from collective cooperation, are always being tested by people who simply do not feel the intrusion of conscience that most people feel. Machiavelli is the philosopher who spoke to this kind of realpolitik most clearly. I would argue game-theory is even more fundamental than conscience and morality. However virtuous and noble, genes that don't replicate leave the genepool. Ethical reasoning seeks to persuade others to hold to unstable equilibria for collective benefit, to take the Prisoner's Dilemma choice of net benefit. That is the reasoning idealistic mode, persuading others to be good serves our mutual interests. But we all know an unreasoned selfishness is there too, testing whether the sacrifices we make to collaborate are truly worthwhile. Socrates had a conscience that overpowered his survival instinct, easily heroised, harder to live. This is the tension between idealistic universalising ethics, and felt morality where we wish to be heroes -even martyrs- but mostly, are not.