The word "sin" appears in this chapter seventeen times. Fifteen of those times, in the original writing, there is something called "The Definite Article" before the word sin.
Stay with me; this is simple. The definite article simply makes the word a noun instead of a verb...calling sin a THING and not an act of iniquity. So, this chapter, along with chapters 7 and 8 are dealing with the sin-nature itself and not acts of sin.
Throughout this study, you will be reading the term, "In Christ," a lot..or some derivitive of the term, i.e., In Jesus, etc. Keep it in mind because it's key.
Also, to properly understand this chapter, the last two verses of chapter 5 must be the beginning.
20 MOREOVER THE LAW ENTERED, THAT THE OFFENCE MIGHT ABOUND. BUT WHERE SIN ABOUNDED, GRACE DID MUCH MORE ABOUND:
21 THAT AS SIN HATH REIGNED UNTO DEATH, EVEN SO MIGHT GRACE REIGN THROUGH RIGHTEOUSNESS UNTO ETERNAL LIFE BY JESUS CHRIST OUR LORD.
The words, "moreover the law entered," is speaking, of course, of the old Testament law. This would be the Ten Commandments along with the Levitical law which expounded on the Ten. We refer to this as the Law of Moses.
The sentence, "moreover the law entered that the offence might abound is speaking of the fact that sin was defined when the law was given. Until the law at the time of Moses, there was nothing that actually told people what was right or wrong.
Many have used this to present the idea that seeing as how there was no law, humanity was not responsible for sin. They use the verse in Romans 5 that says, "For until the law sin was in the world: but sin is not imputed when there is no law. (Romans 5:13)
This verse plainly says that sin was in fact, however, in the world, just not in the form of written law. The only law that had ever been broken before the law was given was when the law was broken in the garden when Adam and Eve ate the fruit that God had ordered for them not to eat.
God gave no more laws after that...not until the law was given. Nevertheless, in-between the time of Adam and Moses, the sin nature still had its effect on humanity, and humanity was seperated from God because of it. We know this because, for one thing, people died between that time of Adam and Moses, even with no law...and it is sin that causes death.
Jas 1:15 - Then when lust hath conceived, it bringeth forth sin: and sin, when it is finished, bringeth forth death.
So, even without law to define sin, it still existed and did its awful thing. Actually, this very chapter (5) tells us this very thing:
Romans 5:14 - Nevertheless death reigned from Adam to Moses, even over them that had not sinned after the similitude of Adam's transgression, who is the figure of him that was to come.
Think of it this way: If I was caught driving one hundred miles an hour, all reckless and all, but there was no law regarding a speed limit, well then, there could not very well be a specific penalty for speeding. Speeding, however, is speeding and it doesn't take a rocket scientist to see when a person is driving reckless and dangerous. That kind of driving will get them killed, and others, even if there is no written law on the matter.
Sin, at its bottom line, is simply self-ism. Self focus. Self desire. Ego. My way instead of God's way. And of course, satan is always pushing for us to go our own way. Our human nature is bent and influenced by the sin nature.
So, the law defined sin, showed us in writing what is right and wrong and also gives us the picture of the type of person God yearns for us to be. The law also does something else: it shows us the devestation of sin and also lets us see that we are short...very, very short regarding adequately keeping such a wonderful law; it shows us we need something; A Saviour, Christ Jesus!
Romans 7:12 Wherefore the law is holy, and the commandment holy, and just, and good.
13 Was then that which is good made death unto me? God forbid. But sin, that it might appear sin, working death in me by that which is good; that sin by the commandment might become exceeding sinful.
The phrase, "but where sin abounded, grace did much more abound," is saying that even though humanity has this sin nature which seperates us from God and dominates our passions and desires, God's grace is stronger.