In order to understand what changes as a result of the tshuvah we have to understand what sin is. This is a long and complicated topic since sinning itself is dependent on a range of theological prerequisites. Instead, as a direction or orientation, a kavanah for this period I would say the following. The worst part of sinning is that it causes one to feel distant from God. One therefore must do tshuvah which is remembering that no matter what you are a child of God. That is what you need to return to.
This, of course, is all in the case of your relationship with God. If you have wronged another person, you have to engage them in a process which will make them whole again, and make your relationship with them whole, before you can stand before and in relationship with God.
Every person sins; it is a given of our imperfect Human condition that we will at times fall short of the mark. Our deeds bring hurt and injury to others. The other given of the Human condition is that we are endowed with free will and can choose to change; we can act to repair the damage we do. Our tradition teaches that the first step of teshuva, repentance, is atonement, or asking forgiveness.
Our Sages taught that only God can seal the process of Teshuvah (repentance). God can grant forgiveness unilaterally for those sins which are limited to our relationship with God. For those sins which involve other human beings, we must first seek and receive forgiveness from them before God will seal that act of repentance. It is hard work.
I find multiple answers to your core question: is there something that remains after God grants forgiveness? The answer depends in large part on what your image of sin is.
Rabbi Samuel Sandmel wrote (We Jews and Jesus, pg 45) that Jews understand sin to be an act or action, and atonement is the acknowledgement of, regret over, and dedication to avoid that act in the future. Forgiveness, as I understand him, implies a repair of the past, but not its erasure.
Sandmel focuses on the future – how will we act from now on. He echoes the thought of Maimonides who teaches that the core of repentance is the sincere resolve not to repeat the act. He writes: "What constitutes complete repentance? He who is confronted by the identical situation wherein he previously sinned and it lies within his power to commit the sin again, but he nevertheless does not succumb because he wishes to repent, and not because he is too fearful or weak [to repeat the sin].” [Mishnah Torah, Laws of Repentance] Here too there is no discussion of whether anything remains “on the record”; the concern is that the act is not repeated.
On the other hand, Rabbi Akiva taught: “Rejoice, Israel! Before whom are you purified? Who purifies you? It is none other than God, as it is said, (Ezekiel 36:25) I will sprinkle clean water over you, and you shall be clean.” (Mishnah Yoma 8:9) Similarly, Isaiah 1:18 teaches: “Come now, and let us reason together, Saith the Lord; Though your sins be as scarlet, They shall be as white as snow.” Here forgiveness equals erasure.
Herman Wouk, in his book, This is My God, agrees that forgiveness erases all record of the sin, but he raises a new concern. He records a conversation he heard between his grandfather and another man over the efficacy of a deathbed confession. His grandfather affirmed the teaching that God is always willing to offer forgiveness in response to sincere repentance. The other man objected, asking what is the value of a life well lived if you can repent for all of your misdeeds at the last second and be forgiven? Wouk's grandfather later explained to his grandson, who thought the objections logical, that “canceling the past does not turn it into a record of achievement. It leaves it blank, a waste of spilled years. A man had better return, he said, while time remains to write a life worth scanning. And since no man knows his death day, the time to get a grip on his life is the first hour when the impulse strikes him.”
Some of our sages believe forgiveness removes the record of our sin while others believe it only repairs the damage of our sin. All agree that the most important outcome is an individual's resolve to live the best life one can.