Isaiah 58 teaches us the true purpose of fasting.
Isaiah 58:6-7 reads, "Is not this the fast that I have chosen? To loose the bands of wickedness, to undo the heavy burdens and to let the oppressed go free, and that ye break every yoke?
Is it no to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? When thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?"
"To loose the bands of wickedness" means that we can fast for strength to overcome our own or to help others overcome bad habits or sins that afflict our lives.
"To undo the heavy burdens" - heavy burdens can represent sins or even physical ailments that afflict our lives.
"To let the oppressed go free" - obviously we do not let our criminals go free on the day of fasting, but in Isaiah's day, "all debts, slaves, and indentured servants were freed" (Ludlow 483). In our day, we can forgive others' trespasses against us. We can endeavor to heal broken relationships that may be oppressing others and ourselves.
"break every yoke" - seems to summarize the true meaning of the fast. We are to seek freedom from sin and to grant freedom where we can.
"deal thy bread to the hungry … cover him” - as we fast today, we save the money we would have used to feed our family and we take that money and give it to the Bishop who uses it to aid the needy within our ward and stake.
"hide not thyself from thine own flesh" - fasting should include giving ourselves to our family. It is a time to be with family and to strengthen or repair familial relationships.
Isaiah 58:13 has a few more reasons for the fast. "… not doing thine own ways, nor finding thing own pleasure, not speaking thine own words." This means we are to do the Lord's will on the day of the fast. We should dedicate our life, that day, to seeking and doing the Lord's will instead of our own. This will help our more fully dedicate our whole life to the will of the Lord.
The blessings of obeying the true fast are outlined in Isaiah 58:8-14.
If we truly obey the fast, the Lord will guide us continually and we shall never thirst. He will make our bones fat and we will be called "the repairer of the breach, the restorer of the paths to dwell in."
L. Tom Perry, “The Law of the Fast,” Ensign, May 1986, 31
Howard W. Hunter, “Fast Day,” Ensign, Nov 1985, 72
Joseph B. Wirthlin, “The Law of the Fast,” Ensign, May 2001, 73
Marion G. Romney, “The Blessings of the Fast,” Ensign, Jul 1982, 2