First, our liberty in Christ is a freedom from the yoke of sin.
Liberty in Christ is not a freedom from spiritual responsibility. It is certainly not any kind of moral autonomy. It is not a release from the divine standard of righteousness. It does not mean we are discharged from our duty to obey the moral law. If you think of liberty in those terms, you need to think again.
In fact, there's a name for that kind of thinking. The theological term for it is antinomianism. Antinomianism is the belief that our liberty in Christ releases us from any and all obligation to the laws and commandments of God. Some will even boldly tell you that the moral law of God has no binding authority for the Christian. But the liberty described here is not freedom from the moral demands of the law.
On the contrary, Scripture clearly teaches that freedom from righteousness is no freedom at all. The apostle Paul says in Romans 6:20 that to be free from righteousness is to be enslaved to sin. Jesus said in John 8:34, "Whosoever committeth sin is the servant of sin."
So fix this in your thinking from the very start: The liberty Christ promises is first of all a liberty from the bondage of sin, and therefore it cannot be a the kind of freedom that nullifies our obligation to the moral law of God.
Romans 6:7 says, "He that is dead is freed from sin." And verse 8 goes on to show that we are dead in Christ and therefore we are liberated from the bondage of sin. Paul's whole argument in Romans 6 is summarized with these words in Romans 6:17-18: "Ye were the servants of sin, but ye have obeyed from the heart that form of doctrine which was delivered you. Being then made free from sin, ye became the servants of righteousness."
So our liberty in Christ, paradoxically, involves a positive kind of servitude as well. It's not an absolute freedom or moral autonomy.
Second, true Christian liberty is freedom from the yoke of the law.
Now this is the point at which many people get confused. Didn't I just say that Christian liberty doesn't erase the moral duties set forth in God's law?
Yes, but the "yoke" or burden of the law doesn't consist chiefly in the standard of moral righteousness it affirms. The moral demands spelled out in the law were not inaugurated by the law, nor is our duty to live in accord with God's moral standard eliminated just because we're "not under the law" covenantally (Galatians 5:18; cf. Romans 6:14-15).
What made the law of Moses a burden was not its moral content per se. In fact, the law's exaltation of righteousness is what made the law holy, just, and good (Romans 7:12). But the law itself could never justify sinners. Even in the Old Testament, believers were justified by faith when a righteousness not of their own merit was imputed to them. That's Paul's whole point in Romans 4. No one was ever saved by his or her own obedience to the law.
The whole point of the law is to condemn sinners and leave them with no hope but the grace of God. The law is a killer. It can only condemn; it cannot save. That is the curse of the law.
And that is the very curse Christ frees us from. Galatians 3:13: "Christ hath redeemed us from the curse of the law, being made a curse for us." He took the guilt of our sin, and He was punished in our place. He died, bearing the guilt of our sin, not His own. So the curse of the law is eliminated. The demands of the law are fulfilled. Our guilt was transferred to Christ, and He paid for it. Now His righteousness is transferred to us.
That's real liberty. "If the Son therefore shall make you free, ye shall be free indeed" (John 8:36).