The Fall of Adam brought a few things along with it. It introduced physical death into the world. Adam was cast out of God’s presence and that became a spiritual death. The Atonement rectifies these two deaths by providing a resurrection to overcome death and also brings each person into God’s presence again at the end of this life, overcoming that spiritual death.
Being born into this world we are surrounded by choices and there is the chance that we choose to break God’s commandments. In fact, it is said in the scriptures that all (except Jesus) have sinned and come short of the glory of God. These are sins, not of Adam’s choice, but of our own. Adam is not responsible for my sins. The Atonement also gives us hope to overcome our own personal sins, if we repent.
Because of the Fall Adam lost immortality, God’s immediate presence, innocence.
The Atonement rectifies death by resurrection, restoring immortality and restores us to God’s presence. We lost innocence, but gained knowledge and ability to choose and the ability to have family, to have children. If we repent we can regain being clean.