What does it mean for God to not remember the sins of those who trust in the atonement of Christ?
Heb 10:17 then He adds, "Their sins and their lawless deeds I will remember no more."
* First of all, what it does not mean?
It does not mean that God will lose memory over it. It's a figure of speech. Not a literal statement that God can actually forget.
God is powerful and almighty, yes. He can do as He please. Nothing is impossible to Him. But God's attributes are never in opposition to each other; they work together in harmony. God would never use His power to cause Him to infringe upon another of His attributes, namely, His omniscience. For God to literally forget is for God to stop being omniscient.
The Corinthians experienced the forgiveness of God but God in inspiring the book of Corinthians clearly remembered the former sinful deeds of the Corinthians:
1Co 6:9 Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived. Neither fornicators, nor idolaters, nor adulterers, nor homosexuals, nor sodomites,
10 nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners will inherit the kingdom of God.
11 And such WERE (past tense) some of you. But you were washed, but you were sanctified, but you were justified in the name of the Lord Jesus and by the Spirit of our God.
God forgave King David but He clearly remembered the sinful deeds of David. When He caused the book of 2 Samuel to be written, the record of David's sins was written down with it as well, by His inspiration.
* Secondly, what does it mean for God not to remember sins?
It's a figure of speech that God will never hold it against anyone who trusts in Christ because He held it against Christ on the cross on the trusting sinner's behalf. When He sees the trusting sinner's sins, He now sees Christ assuming it, bearing it, taking it upon Himself, with His blood on it.
2Co 5:21 For He made Him who knew no sin to be sin for us, that we might become the righteousness of God in Him.
God now treats the trusting sinner as though he never sinned. He now treats him as righteous before His sight.
