Matthew 17:18 And Jesus rebuked the demon, and it came out of him; and the child was cured from that very hour. 19 Then the disciples came to Jesus privately and said, “Why could we not cast it out?” 20 So Jesus said to them, “Because of your unbelief; for assuredly, I say to you, if you have faith as a mustard seed, you will say to this mountain, ‘Move from here to there,’ and it will move; and nothing will be impossible for you. 21 However, this kind does not go out except by prayer and fasting.”
"Fasting confirms our utter dependence upon God by finding in Him a source of sustenance beyond food." (Dallas Willard)
Jesus' disciples could not help a child that was brought to them. They BELIEVED that they could help the child, but were unable to do so. They asked Jesus, “Why could we not cast it out?” Jesus said, "Because of your unbelief."
Wait a minute! If the disciples did not believe, why did they try to cast out the demon?
Unbelief is not only a lack of belief or faith, it is also a lack of preparation.
Prayer & fasting helps "this kind" to "go out." I don't think the text necessarily means "this kind" of demon (even though some Bible versions indicate this). I think Jesus is talking about "this kind" power and presence of God going forth from (or out of) those who prepare themselves to minister to people. The real subject of this text is not demons, but faith in God.
Regardless of your interpretation, it is clear that prayer and fasting help us go to a higher level of functioning by faith. Part of that higher level comes from not placing our usual emphasis on food and things natural/earthly. Faith is more than believing. Faith is acting on the Word of God.
Prayer is our most important spiritual activity, and fasting enhances that activity.
