v. 4: “Everyone who sins breaks the law; in fact, sin is lawlessness.”
This seems pretty straightforward to me. The law is there to dissuade us from sinning and to protect us from being the victim of someone else’s sin. When we sin, we’re breaking the law–and not only laws like the Constitution or state laws or even your parent’s rules, but God’s laws as well.
v. 5: “But you know that He appeared so that He might take away our sins. And in Him is no sin.”
Jesus is pure. There is, never was, and never will be any sin in Him. He is perfect. And because He is perfect, He was able to come down to earth and die to take away our sins for us. You know how in the Old Testament people would sacrifice a lamb as atonement for their sins, and that the lamb had to be without spot or blemish? Jesus was the Lamb of God–perfect and blameless before Him–and He atoned for our sins for all of eternity. That’s why He came to earth.
v. 6: “No one who lives in Him keeps on sinning. No one who continues to sin has either seen Him or known Him.”
Since Jesus is without sin, you cannot live like Him and keep sinning. There is no room for sin in the lifestyle He sets up for us. And if you keep sinning, you can’t have truly seen Him, because if you did see Him you would be so overwhelmed and overjoyed that you wouldn’t even consider sinning again. I think that in a way, if you fall away from God into sin, you have never truly known Him, either.