What does having a “seared conscience” mean? What is a “seared conscience?”
The Knowledge of Sin
You don’t have to tell a 6-year-old when they’ve done something wrong. They already know that some things are right and somethings are wrong. Children are just like adults in the sense that they have an internal moral compass, so to speak, and this tells them that what they are doing is sin or it is not sin. Even without having a Bible or knowing the Word of God, people know that some things are wrong. The Apostle Paul says as much when referring to unsaved people (Gentiles), and says that the “Gentiles who do not have the Law do instinctively the things of the Law, these, not having the Law, are a law to themselves, in that they show the work of the Law written in their hearts, their conscience bearing witness and their thoughts alternately accusing or else defending them, on the day when, according to my gospel, God will judge the secrets of men through Christ Jesus” (Rom 2:14-16). In other words, we have no excuse (Rom 1:20) because even unbelievers are simply suppressing the knowledge of God (Rom 1:18) and know that He exists.
The Spirit’s Conviction
When a person is brought to repentance by God (2nd Tim 2:25), the Holy Spirit begins working in that person’s life to convict them of their sins and to make them see their desperate need for the Savior. Before Jesus returned to the Father, He promised a Helper or an Advocate, and that “when he comes, he will convict the world concerning sin and righteousness and judgment” (John 16:8), and so, “it is to your advantage that I go away, for if I do not go away, the Helper will not come to you. But if I go, I will send him to you” (John 16:7). So the Spirit of God convicts the world of sin and of God’s righteousness and judgment. We can tell lost people about the wrath of God for those who reject Jesus Christ, but in their hearts, they already know He exists, but they don’t want to give up their sins, so it is not us who convict the world of their sins, it is the Helper, because “when he comes, he will convict the world concerning sin and righteousness and judgment” (John 16:8). That’s why a person who comes to faith in Christ  doesn’t come to Christ on his or her own. The Father is drawing them (John 6:44) by the Spirit of God and comes to faith by the Word of God (Rom 1:16; 1st Cor 1:18).
A Seared Conscience
You know what searing is, right? You can sear roast beef in a pan before you broil it and it tastes better. Fresh hamburger is seared when it’s put on the grill. Whatever is seared is burnt and is not the same as it was before, and so it is with the conscience. The Apostle Paul wrote to Timothy that “the Spirit explicitly says that in later times some will fall away from the faith, paying attention to deceitful spirits and doctrines of demons, by means of the hypocrisy of liars seared in their own conscience as with a branding iron” (1st Tim4:1-2). In other words, if we suppress the conviction of the Spirit of God and resist Him and keep on sinning, after a time, the conscience is so seared or burnt that we cannot hear the Spirit speak to our conscience anymore. That’s because God has given every one of us His light, so even with “their conscience bearing witness and their thoughts alternately accusing or else defending them” (Rom 2:15), they simply suppress this knowledge (Rom 1:18), and eventually, the conscience cannot hear what the Spirit of God is telling them. The more a person suppresses (ignores) the voice of the Spirit, the harder it is for the Spirit of God to speak to them about their sin. If this continues, the conscience will become like a callous on a hand…it will not feel anything anymore. By tuning out the Spirit of God, we are making it harder each time for the Spirit of God to speak to us. In time, the conscience will be so seared that we cannot even hear the Spirit anymore, and that will surely bring disaster.
A Good Conscience
If we have responded to the Spirit of God’s prompting, we will have a clear conscience, but if we don’t, and we choose to disobey, then God’s Spirit will inform us that we are sinning by convicting us. For example, “whoever knows the right thing to do and fails to do it, for him it is sin” (James 4:17), because they know what is right and what is wrong, but yet don’t do it. Another example is “if anyone has the world’s goods and sees his brother in need, yet closes his heart against him, how does God’s love abide in him” (1st John 3:17)? I would say, it doesn’t, because if he was a child of God, he would feel compelled to help his brothers and sisters when they’re in need. What would you and I do if we saw “a brother or sister is without clothes and daily food” (James 2:15)? Would we say, ‘Go in peace, be warmed and filled,’ without giving them the things needed for the body, what good is that” (James 2:16). Instead of helping them, would we just say, “I’ll pray for you?” That would be of no real help, and it might show that we are either quenching the Spirit of God, or we don’t have the Holy Spirit in the first place, and thus, we might not be saved at all!
If your conscience has ever convicted you of doing something wrong, then listen to your conscience, because the Holy Spirit might be trying to tell you something. If you ignore it long enough, you’ll eventually stop hearing His voice, and then there is the danger that God may give you up to a reprobate mind, which is a mind that no longer desires obedience and cannot do that which is right. This is why for some, “God gave them over in the lusts of their hearts to impurity, so that their bodies would be dishonored among them” (Rom 1:24), and “gave them over to degrading passions; for their women exchanged the natural function for that which is unnatural, and in the same way also the men abandoned the natural function of the woman and burned in their desire toward one another, men with men committing indecent acts and receiving in their own persons the due penalty of their error” (Rom 1:26-27), and “just as they did not see fit to acknowledge God any longer, God gave them over to a depraved mind, to do those things which are not proper” (Rom 1:28). That sealed their fate. If we keep on sinning once we’ve been saved, then our conscience can also be seared, as with a hot iron, and the Spirit can no longer tell us when we are sinning. That’s a very dangerous place to be.
Related reading for you: How to Hear the Voice of the Holy Spirit in Your Life 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), Crossway Bibles. (2007). ESV: Study Bible : English standard version. Wheaton, Ill: Crossway Bibles. Used by permission. All rights reserved.