The conscience is a neuropsychological mechanism that serves to restrain and re-focus a person's intent and actions. The conscience primarily involves the histaminergic function of the caudate nucleus, and the glutamatergic function of the anterior cingulate cortex, working together with eachother. What happens is that the caudate nucleus sustains the activity of the anterior cingulate cortex, creating a sustained aversion to something that is located elsewhere in the brain. The same mechanism is also involved in obsessive-compulsive disorder and obsessive-compulsive personality, but in those cases, it serves different ends.
Beyond that core mechanism, the definition of "conscience" is variable.
The definition may or may not include empathy, and thus the mirror neurons of the inferior parietal cortex. Such a type of conscience may be called an "empathy conscience" or "empathic conscience" for greater specificity. Two other types of conscience are the health conscience, in which a person does something because it is healthy, or does not do something because it is unhealthy; and the safety conscience, in which a person does something to improve safety, or does not do something because it is dangerous.
The strength of the conscience varies between individuals, due to differences in the genetic alleles that regulate the relevant neural mechanisms. In the "OCEAN" system of temperament psychometrics, the letter "C" stands for "conscience", and signifies the strength of this neural mechanism that is fundamental to a person's personality.