What does Matthew 17:21 mean?

Most modern translations don't include these words in book of Matthew. The phrase does not appear in the most reliable manuscripts available. A reference to prayer is included in Mark's account, with a comment on fasting also appearing as a later footnote (Mark 9:29).

Jesus' words, from Mark, imply that some demons require additional effort to exorcise. In the prior verse, from Matthew, Jesus said faith was the heart of the issue for the disciples' failure to cast the demon out (Matthew 17:17). He did not say their primary issue was a lack of prayer and fasting. The true error—the foundation of their failure—was they did not sufficiently trust the power of God to work through them. Jesus was clear that nothing would be impossible for them if they had faith even as small as a mustard seed (Matthew 13:31–32; 17:20).

Still, prayer and fasting are expressions of faith. It would never be wrong for a Christian to pray or even to fast when trying to accomplish the will of God. It would be wrong, however, to believe that the actions of prayer and fasting are themselves sources of power. Those things are merely expressions of faith in God. His power is what accomplishes the will of God, such as for demons to be removed.