Where the phrase comes from
The exact phrase appears in James's instructions to Christians facing illness. A sick person is to call for the elders of the church, who pray over them in the Lord's name. James says that the prayer of faith will save the sick and that the Lord will raise them up, while also speaking of forgiveness where sin is involved (James 5:14-16).
In this setting, the prayer of faith is not a private attempt to summon healing by sheer certainty. It is the church praying dependently, in Jesus' name, and trusting the Lord to act. The focus is on God, not on the strength of the person praying.
And the prayer of faith shall save the sick, and the Lord shall raise him up; and if he have committed sins, they shall be forgiven him.
Faith trusts God himself
Biblical faith means relying on God and his character. When Jesus taught his disciples to pray believing, he was calling them to trust God, not to treat prayer as magic (Mark 11:24). Faith takes God seriously because he is able, good, and faithful.
That trust can include asking boldly for healing, provision, wisdom, reconciliation, or strength. Yet it also listens to what God has revealed. John says believers can have confidence as they ask according to God's will (1 John 5:14). Faith does not demand control. It brings a real request and entrusts it to a real Father.
And this is the confidence that we have in him, that, if we ask any thing according to his will, he heareth us:
It is not a guarantee of the outcome we choose
This can feel difficult, especially when someone is seriously ill. James encourages the church to pray expectantly, and Christians should not stop asking God to heal. Still, Scripture does not say that every sincere prayer receives the exact answer requested in the exact way requested.
Paul pleaded with the Lord about a painful weakness, but God answered by showing that his grace was sufficient and his power worked through Paul's weakness (2 Corinthians 12:8-9). That was not rejection. It was a different answer, one that kept Paul close to Christ. So a delayed healing or an unanswered request does not automatically mean someone lacked faith.
And he said unto me, My grace is sufficient for thee: for my strength is made perfect in weakness. Most gladly therefore will I rather glory in my infirmities, that the power of Christ may rest upon me.
How to pray with faith
Start plainly. Tell God what is happening and ask specifically for what you need. If illness is involved, consider asking trusted church leaders to pray, as James describes (James 5:14). Confess known sin honestly too, not as a way to earn God's help, but because walking in the light matters (James 5:16).
Then keep coming to God. Ask for wisdom when you do not know what to do, trusting that he gives generously rather than shaming those who ask (James 1:5-6). Pray with hope, receive help from God's people, and leave room for the Lord's answer to be wiser than your own. Faith says, "God, you can do this, and I will keep trusting you."