conscience: the inner sense by which a person judges their own conduct as right or wrong and bears witness for or against themselves
The word is built from parts meaning "with" and "to know," so at root it names a kind of inner co-witness: a person knows something about their own conduct, and part of them stands back and testifies to it. In the New Testament this inner witness most often weighs the moral quality of what a person has done or is about to do, speaking up for them when they have acted rightly and against them when they have not.
Two shades appear within this. Sometimes conscience is active, bearing witness in the moment: it accuses, it confirms, it can be pointed to as proof of honest dealing before God and other people. Other times the writers speak of a good or clean conscience as a settled possession, a standing mark of integrity that goes hand in hand with sincere faith. They also warn that it can be wounded, defiled, or hardened until it no longer registers wrongdoing at all.
Readers should be careful not to read the modern idea of conscience back into these texts. Today conscience is often imagined as an inner voice of God or an infallible private guide. The biblical writers treat it more modestly, as a witness that reports on conduct against a standard, and one that can be poorly informed or damaged.