The Bible seems to speak of four levels of the efficacy of prayer.   Usually, only the first one is given serious consideration.

1. Prayer has an effect on the one who prays. Prayer enables fresh initiative, motivating the pray-er to redirect thought and life toward those persons or things for which we pray. Our sights are sharpened, our wills empowered, or healing takes place at some level within us. If nothing else, it directs our thoughts toward someone in healthy ways. As is said, “energy flows where direction goes.”
2. Prayer has an effect on the relationship between the one who prays and God. In and through prayer the relationship is enhanced and made more mature. Yet all too often change is thought to occur only on the human side of the relationship. People think God in relationship never changes in any respect. But the Bible claims that God is also affected by prayers offered.
3. Prayer has an effect on God. Much here depends on our image of God. It is often thought that God cannot be moved at all by any human words or deeds, and that God certainly cannot be persuaded by anything humans have to say. Yet many biblical texts claim that prayers have an effect on God and contribute something to the way in which God relates to the world and to the shape of the future. Prayers of repentance make for rejoicing in heaven (Luke 15:7). Or, consider Psalm 22:3: God is “enthroned upon the praises of Israel.” God’s rule is furthered or God’s reputation is enhanced by our praising prayers. Even more, God is genuinely moved by our prayers, perhaps even persuaded by our prayers (see Luke 11 and 18). The Bible claims that prayer makes a difference to God and has an effect on what God accomplishes in the world.
4. Prayer has an effect upon persons or situations for which one is praying. Somehow the power of God is made more available for a third-party situation because we have prayed (intercession). This is true whether or not that third party is aware of being prayed for. In this sense, prayer is a form of mission in and through which God accomplishes things in the world beyond the hearing range of our words and the doing range of our actions.