First, sin is a failure to do what we are obligated to do. God as Creator has given us responsibilities for which He holds us accountable. If we fail to carry out these responsibilities, we incur a debt.
Next, sin is an expression of enmity, a violation of the personal relationship human beings are supposed to have with their Creator. When we sin against God we break that relationship. We express not love and devotion to Him but rather a kind of hostility that is serious and must be addressed.
Finally, the Presbyterian Westminster Shorter Catechism says that “sin is any want of conformity unto or transgression of the law of God.” In modern English that means any time we break the law of God, we sin. If a crime has been committed, then we have to deal with penal sanctions. If a debt has been incurred, then we have to come to grips with what we all pecuniary sanctions.
Enmity has to do with personal relationships, and these need to be healed. If I steal $1000 from a man, I may not feel that I owe him anything, but I do. I may not feel that I have committed a crime, but I have. I may not feel that Ive acted in a hostile fashion toward him, but he feels it. Whether I realize it or not, a bad situation exists, one that must be corrected or else I will suffer for it.