As I have the opportunity to fast for members of my family, I am reminded of at least three reasons why fasting and prayer are more efficacious than normal prayer. For one, as we are obedient to something that is a challenge, the Lord has more room to bless us. Second, because while we go without food or drink, we are driven to consider our need, and in this He is the resource of our aid, not food or drink, but Him. As we come unto Him for our needed spiritual and physical help, we open up the door to greater communion and unity.
Third, because of our submission to the Spirit, our wills are more aligned to His, and we recognize and honor Him as our sustainer and law giver. We promise to do His will and yield ourselves unto Him. It is all three of these reasons and more, that give fasting a more purifying, purposeful and effective result.
A forth one to consider, is when I am struggling to get through to keep my fast, the actual suffering itself, with the persons or situations in mind, will experience a relief of their suffering, as the trials they are experiencing are then transferred with love, onto the one(s) fasting for their relief. The fact is, the faster or fasters, are drawing unto the Lord, and it is Christ who takes the pain and burden, as it is He who does so through the atonement for everyone anyway. We just need to let Him. If someone is in need of extra help, we can be the means for them, to share the load, bringing us closer together, and letting Christ do His part.
It is a communal effort, in which loved ones combine, to cover an ailment of the one or many, and give them the strength to make it through. In other words, it is a labor of love.