As I mentioned the other day, Joseph Smith cited faith in the Lord Jesus Christ as the first principle of the gospel. The second, he says, is repentance (Articles of Faith 1:4).
Repentance is a remarkable gift offered us through the atonement of Jesus Christ. It is in my mind what allows us to change. We teach our children that it's a process – recognize that you've done wrong, feel remorse for the mistake, confess the error to God (and to others who might have been hurt), restore what was lost in the mistake, and don't repeat the error.
I was teaching a class in church a few years ago about repentance. I had drawn a picture of the straight and narrow path (the Savior taught that baptism sets us on that path; see Matthew 7:14, Matthew 3:15) on the board. I asked what the first thing we would do when we realize we are off the path. The answer: Stop! Then we'd try to find our way back to the path, and repentance is the way to do that.
One might think of repentance as "turning" back to the Lord.
However we think of it, repentance allows us to realign ourselves with God. And it's made possible by the sacrifice of Jesus Christ. It is, to me, part of His gift to us (which also includes His perfect example and His resurrection which gives us power over death).
In a world where self-help books line bookstore shelves, repentance is, to me, what makes it possible. Repentance is what allows us to change, to abandon our past mistakes, to leave guilt behind, and to move forward better men and women than when we started.
The other thing I've found in my own life is that I cannot do it alone, and this is why repentance is not simply another label for self improvement. Instead it is the vehicle through which self improvement is possible. Changing without repentance has not worked for me. The acknowledgement of the need for a Savior in my life to help me overcome my weaknesses has been a key for my own progress along that path.