Matthew 17:19-21 "Then came the disciples to Jesus apart, and said, Why could not we cast him out? And Jesus said unto them, Because of your unbelief: for verily I say unto you, If ye have faith as a grain of mustard seed, ye shall say unto this mountain, Remove hence to yonder place; and it shall remove; and nothing shall be impossible unto you. Howbeit this kind goeth not out but by prayer and fasting."
What comes out only by prayer and fasting? The spirit? No. He was referring to unbelief. It's unbelief that only goes out by prayer and fasting. He fully expected the disciples to cast that spirit out, on the spot, or He wouldn't have rebuked them saying in verse 17, saying, "O faithless and perverse generation, how long shall I be with you?" The issue wasn't casting a spirit out, it was their unbelief.
Prayer and fasting brings us from a place of unbelief - where my mountains refuse to move, where everything seems impossible to me - to a place where nothing is impossible for me.
When we fast, we are enforcing the positional truth that the sin nature was crucified with Christ and our flesh no longer has the power to rule over our spirit. Our fasting doesn't move the devil, he's not the one with our problems. Fasting doesn't move God, it moves us into a place where we can receive from God.
Fasting destroys the hold that the flesh has had on our lives, that has defeated us time and time again, year after year. Lies that tell us things will never get better, or that we will never accomplish more than we've already accomplished, that this is it for us.
Fasting has the same effect on our flesh as it had on Jesus' flesh: it braces us against the temptations of the devil and helps us shut down the flesh by enforcing the perfect standing Jesus has already given us. As the flesh loses ground, the peace of God can begin to rule in our lives.
You choose. A meal. Or a mountain. Which would you rather do without?