As used in the scriptures, to atone is to suffer the penalty for sins, thereby removing the effects of sin from the repentant sinner and allowing him or her to be reconciled to God. Jesus Christ was the only one capable of carrying out the Atonement for all mankind. Because of His Atonement, all people will be resurrected, and those who obey His gospel will receive the gift of eternal life with God.I'd like to narrow the scope of my discussion to the earthly ramifications of the Atonement, or how people use the Atonement in their lives. In the most traditional sense, we use the Atonement to repent of our sins. It is a wonderfully cleansing process to think back on the things I've done wrong and be healed--it enables me to let things go and forgive myself.
Additionally, LDS folks often talk about the Atonement enabling Christ to know all our sorrows and joys; He feels perfect compassion. This is nice because we will always have someone to turn to for comfort, no matter what we are experiencing.
I recently utilized an aspect of the Atonement which is new for me--it doesn't strictly fall under either of these categories. A motley of events have lead me to feel mild anger, a hesitation to do what's right, and dislike of specific individuals. These are all mental and spiritual burdens which can be lifted through mechanisms closely related to the two other usages of the Atonement. In my case, the negative emotions were replaced by love, which was a mixture of repentance and experiencing the compassion of Christ.
It's old hat to use one's relationship with God to improve oneself, but I had never framed it in this way before: negative emotions can be relieved as soon as we acknowledge them as unwanted and seek healing. The earthly ramifications of any of these mechanisms can probably be achieved through other means as well, but I thought I'd share a little bit about my method of healing.