James uses this term in a passage that is not easily understood (5:15). It seems to promise more than it always delivers: divine healing in response to “the prayer offered in faith” by the elders of the church.
That sounds simple enough, but there are two additional factors: anointing with oil, and confession of sin. The sickness for which healing is promised evidently is caused, at least in part, by sin. Possibly, it is heart sickness. In any case, to the anointing with oil is added the confession of sin. The prayer of faith evidently takes these elements into consideration.
There seems to be no guarantee that the prayer of faith will work, no matter how sincere, and no matter that it follows confession of sin and anointing with oil. All we can know for certain is that God hears us, and that He will give us what He thinks we need. Giving us what we request every time would work against our best interests.