The English word "conscience" is used thirty-one times in the KJV New Testament. It comes from the Greek suneidesis (Strong's Concordance #G4893), which means "moral consciousness" (Strong's) or the moral voice in humans that helps us distinguish between what is good and bad and prompts us to do what is right and reject the wrong (Thayer's Greek Definitions). A clean heart not only can guide us as it relates to something in the present, it can also convict us of something we did wrong in the past.
God has placed, in each human, a conscience with a basic comprehension of what is fundamentally right and wrong. He has given it to us to guide, but not override, our actions. It has the ability to lead people, even those who oppose the Gospel, to do what is right (John 8:3 - 9). The Apostle Paul confirms the fact that humans who never directly received God's commandments, like the ancient Israelites, still possess a basic intrinsic moral code or law that judges what they do.
14. For when the Gentiles (non-Jews), which do not have the law (Ten Commandments, etc.), practice BY NATURE the things contained in the law, these who do not have the law are a law unto themselves; 15. Who show the work of the law written in their own hearts, their consciences bearing witness, and their reasonings also, as they accuse or defend one another (Romans 2:14 - 15).
The conscience each of us possesses is not static. It can be changed by altering the rules (beliefs and principles) under which it operates. We have the power to defile it (1Corinthians 8:7, Titus 1:15), suppress it or even get rid of it entirely (1Timothy 4:2). Christians, according to the Apostle Paul, can have one that is strong or weak based upon their understanding of God's truth (1Corinthians 8:4, 7, 9 - 12). Those who have one which is weak can, through the power of the Holy Spirit, have it educated and strengthened to more fully reflect the Father's will (Philippians 3:15).
How important is it?
Paul considered a clean conscience, even among those new in the faith, to be an essential part of being a Christian. He admonishes those who have a greater understanding of the truth to be concerned, out of love, about how some of their actions might adversely affect "weaker" believers. The apostle emphatically states that it is a sin to lead others to defile their conscience (meaning to go against it and bring guilt), as well as going against the one we have (see 1Corinthians 8, 10:27 - 32).
Maintaining a good conscience is important to all believers, especially to those who are active in God's work (1Timothy 1:18 - 19). This is why Christians are commanded to obey (as long as it is not against God's will) the civil authorities they live under (Romans 13:1 - 5). Those who do good with a clean heart, yet are unjustly persecuted and accused of evil, receive praise from the Father (1Peter 2:19 - 21, 3:16 - 17).
It should be noted that one of the primary differences between the Old and New Covenants is that the Old could not make a person's heart clean before the Eternal. It is only under the New Covenant, made possible by Christ's shed blood, that our hearts can be purged of guilt (Hebrews 9:9, 14, 10:4, 11, 22).
Freedom to lie
Sadly, there have always been those (especially in the end time we now live in) who, after being enlightened with the truth, reject it (1Timothy 4:1). In their rejection, they spread lies and false doctrines concerning what the Bible teaches. How can former believers feel so FREE in spreading errors?
Those who apostatize from the faith and begin to spread lies can do so because their hearts have been "cauterized (burned or seared) with a hot iron" (1Timothy 4:2). Clearly, a person can defile and work against their conscience to such an extent that it no longer functions as a gauge of right and wrong. They destroy what God has given them and, consequently, are free to pursue whatever evil they wish unhindered by any guilt or remorse.
A conscientious objector (CO) is someone who refuses, on moral or religious grounds, to take up arms in a military conflict or to serve in a country's armed services (dictionary.com). Those who take such a stand based on their conscience, however, may be required to serve in noncombat positions. Religious groups whose members have refused to participate in armed combat include the Seventh-day Adventists, Jehovah's Witnesses, Amish, Mennonites and others (Wikipedia).
Heavyweight boxer Muhammad Ali is one of the most well known religious objectors to fighting in a war. In 1966 he was arrested after refusing, out of conscience, to be drafted into the U.S. military. He was soon stripped of his boxing titles after being found guilty of draft evasion. The U.S. Supreme Court unanimously overturned Ali's conviction in 1971 (Wikipedia).
Conscience money is a voluntary, usually anonymous, payment made for an obligation that was evaded (e.g. taxes) or a wrong that was committed. Started in 1811 A.D., the United States Treasury maintains a fund specifically designated to receive contributions from people who feel they have stolen from or defrauded the government (Wikipedia).