What is an "offence" according to the Word of God?
It's something that trips up someone so that he falls into sin or unbelief. The New Testament uses it as a noun. "Therefore let us stop passing judgment on one another. Instead, make up your mind not to put any stumbling block or obstacle in your brother's way" (Romans 14:13; Romans 14:20; 1 Corinthians 8:9). It also uses it as a verb. "It is better not to eat meat or drink wine or to do anything else that will cause your brother to fall" (Romans 14:21; 1 Corinthians 8:13).

The verb use is very instructive. When it's active, it means "to cause to stumble or fall." For example, "But if anyone causes one of these little ones who believe in me to sin, it would be better for him to have a large millstone hung around his neck and to be drowned in the depths of the sea" (Matthew 18:6).

But when it's passive, it means "to stumble over, to take offence." But in this case, the blame isn't on the "stumbling block." It's on the one who stumbles. For example, "And they took offence at him" (Matthew 13:57). Literally, "they stumbled over him." Jesus was the stumbling block, but he didn't sin. It was their own fault that they stumbled. They "took offence...because of their lack of faith" (Matthew 13:58).

This is a very important distinction. In other words, it's a sin to give offence. But it's also a sin to take offence.

Romans 14:13 - Therefore let us not judge one another anymore, but rather resolve this, not to put a stumbling block or a cause to fall in our brother's way

Romans 14:19-21 - Therefore let us pursue the things which make for peace and the things by which one may edify another. Do not destroy the work of God for the sake of food. All things indeed are pure, but it is evil for the man who eats with offence. It is good neither to eat meat nor drink wine nor do anything by which your brother stumbles or is offended or is made weak.

1 Corinthians 8:8-13 - But food does not commend us to God; for neither if we eat are we the better, nor if we do not eat are we the worse. But beware lest somehow this liberty of yours become a stumbling block to those who are weak. For if anyone sees you who have knowledge eating in an idol's temple, will not the conscience of him who is weak be emboldened to eat those things offered to idols? And because of your knowledge shall the weak brother perish, for whom Christ died? But when you thus sin against the brethren, and wound their weak conscience, you sin against Christ. Therefore, if food makes my brother stumble, I will never again eat meat, lest I make my brother stumble.

Jesus Warns of Offences
Matthew 18:6 - "Whoever causes one of these little ones who believe in Me to sin, it would be better for him if a millstone were hung around his neck, and he were drowned in the depth of the sea.

Matthew 13:57 - So they were offended at Him. But Jesus said to them, "A prophet is not without honour except in his own country and in his own house."

The Sin of Giving Offence
When Paul talks about strong and weak brothers in Romans 14-15 and in 1 Corinthians 8-10, he warns against the sin of giving offence. "When you sin against your brothers in this way you wound their soul.

The Sin of Taking Offence
The people of Jesus' hometown "took offence at him." Jesus was a stumbling block, but not in the sense that he committed the sin of giving offence. Rather, he was a stumbling block in the sense that he was the occasion for their sin of taking offence. They probably blamed Jesus. But in reality, the reason they took offence was "their lack of faith" (Matthew 13:57-58). The sin was theirs, not his. When you sin in this way by taking offence you wound your own soul.

Conclusion
It is a sin to give offence, but it is also a sin to take offence.

I've committed both of these kinds of sins-I've both given and taken offence at varying points in my Christian life. How thankful I am that I have a faithful Savior who has loved me and received me, whose righteousness covers me, and whose Spirit is sanctifying me.

Easton's Bible Dictionary
Offence:
1. An injury or wrong done to one (1 Samuel 25:31; Romans 5:15). Romans 5:15 - But the free gift is not like the offence. For if by the one man's offence many died, much more the grace of God and the gift by the grace of the one Man, Jesus Christ, abounded too many.
2. A stumbling-block or cause of temptation (Isaiah 8:14; Matthew 16:23; 18:7). Greek skandalon, properly that at which one stumbles or takes offence. The "offence of the cross" (Galatians 5:11) is the offence the Jews took at the teaching that salvation was by the crucified One, and by him alone. Salvation by the cross was a stumbling-block to their national pride.

Isaiah 8:14 - He will be as a sanctuary, But a stone of stumbling and a rock of offence to both the houses of Israel, as a trap and a snare to the inhabitants of Jerusalem.

Matthew 16:23 - But He turned and said to Peter, "Get behind Me, Satan! You are an offence to Me, for you are not mindful of the things of God, but the things of men."

Matthew 18:7 - Woe to the world because of offences! For offences must come, but woe to that man by whom the offence comes!

Galatians 5:11 - And I, brethren, if I still preach circumcision, why do I still suffer persecution? Then the offence of the cross has ceased.