"We tend to think of the results of repentance as simply cleansing us from sin. But that is an incomplete view of the matter. A person who sins is like a tree that bends easily in the wind. On a windy and rainy day, the tree bends so deeply against the ground that the leaves become soiled with mud, like sin. If we focus only on cleaning the leaves, the weakness in the tree that allowed it to bend and soil its leaves may remain. Similarly, a person who is merely sorry to be soiled by sin will sin again in the next high wind. The susceptibility to repetition continues until the tree has been strengthened.
"When a person has gone through the process that results in what the scriptures call a broken heart and a contrite spirit, the Savior does more than cleanse that person from sin. He also gives him or her new strength. That strengthening is essential for us to realize the purpose of the cleansing, which is to return to our Heavenly Father. To be admitted to his presence, we must be more than clean. We must also be changed from a morally weak person who has sinned into a strong person with the spiritual stature to dwell in the presence of God. We must, as the scripture says, '[become] a saint through the atonement of Christ the Lord.' (Mosiah 3:19.) This is what the scripture means in its explanation that a person who has repented of his sins will 'forsake them.' (D&C 58:43.) Forsaking sins is more than resolving not to repeat them. Forsaking involves a fundamental change in the individual."
- Dallin H. Oaks, "Sin and Suffering," Ensign, July 1992, pp. 70-73
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I thought the analogy Elder Oaks offered of the tree bending in the wind was an interesting one. When the trunk is not strong, it bends until the leaves become dirty in mud. You can wash the leaves, but when the next wind comes, they just get dirty again. You need not only to wash the leaves but also to strengthen the trunk if you want to truly solve the problem.
And so it is with us and our attempts to repent and progress. We must not simply stop a sin; we must grow in strength so that it doesn't recur. We don't just stop a bad habit or behavior; we replace it with a good one. We must not superficially change; we must change deeply, change "to a state of righteousness" until we become a "new creature" (Mosiah 27:25-26); and that happens only through the grace and blessing of the atonement of Christ.