From Gerald N. Lund and the book “A Year of Powerful Prayer’:
One day a father brought a child who was having seizures. This father begged the Savior to bless his son, saying he had taken him to the disciples, but they couldn’t heal him. Jesus blessed the child and a immediately the boy was healed. (see Matthew 17:14–18)
Afterward, the disciples, troubles by their inability to heal the child, asked Jesus. “Why could we not cast him out?” (Matthew 17:19). The Savior” said that it was because they didn’t have sufficient faith. But then added a significant comment: “Howbeit, [nevertheless], this kind goeth not out but by prayer and fasting” (Matthew 17;21)
Some challenges, some circumstances, and some conditions are soft such magnitude and are so serious that an extra measure of spiritual is required to overcome them. To it we add fasting. There is something about fasting that generates greater spiritual and deeper spiritual sensitivity. Perhaps it comes from deliberately and consciously putting the flesh in subjection tot he spirit. One obvious benefit of fasting is that the pangs of hunger constantly remind us of the issue at hand. We find ourselves praying about it all day long, not just in the morning and evening.
In short, fasting is a way to intensify the process of importuning the Lord. It generates the power we need to finally bring down the powers of heaven in our behalf. ~~Gerald N/ Lund: A Year of Powerful Prayer (Salt Lake City: Deseret Book, 2013) p.154-55