Sin is doing what is wrong, as well as not doing what is right. It is breaking the Law of God (1 John 3:4). In other words, it is doing what is against God's will. If he says "Do not lie," and you lie, then you have sinned. If he says "Do not steal," and you steal, then you have sinned. And, according to God, sin separates you from him (Isaiah 59:2).
Sin is an offense to God's character. Because God cannot lie (Titus 1:2), it is wrong for you to lie. Because God cannot steal, it is wrong for you to steal. Right and wrong, then, is a manifestation of the character of God. God is holy; he cannot sin. Sin offends him personally because they are his laws of right and wrong you are breaking. If you have offended him, then you must find a way to "unoffend" him. The problem is that you can't, but he can and has, by offering his Son, Jesus Christ, on the cross as a sacrifice for sin.