Hebrews 4:14-16 "Therefore, since we have a great high priest who haspassed through the heavens, Jesus the Son of God, let us hold fast our confession. 15 For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yetwithout sin. 16 Therefore let us draw near withconfidence to the throne of grace, so that we may receive mercy and find grace to help in time of need."
Introduction: What unbelievers outside of Jesus Christ understand about prayer
People outside the Christian faith generally pray only for two reasons: out of fear or out of need. When an unbeliever calls out to God in repentance, God will hear such prayers due to the fact that the Spirit of God has already been at work (see for instance the sailors in the Book of Jonah and 2 Timothy 2:24-25). In other occassions where God responds to unbelievers, it is out of God's choice to respond, being that He is not obligated to unbelievers' prayers.
At best, this is what natural unbelieving man is able to understand about prayer, namely fear and need. The thought of enjoying God never crosses the non-Christian's mind, due to the fact that outside of Jesus, people can only know about God but not know Him (Acts 17:24-25; 1 Corinthians 2:9,14). Such general observations underscore why we need to look to Jesus in understanding how to pray and why we pray. Jesus alone connects human beings by faith to God. Jesus Christ is the fulness of God's revelation in human flesh. When by the Spirit's working through the specific revelation (i.e the Gospel in the Bible) people respond in saving faith and thus are reconciled to God. Since Jesus Himself, being God, came as a man and retains such humanity to connect God to the Christian, the Christian can now know God and experience Him on a personal level.
What makes prayer unique in Christianity and the Gospel: Personal connection to God through Jesus Christ
What makes the Gospel and Christianity unique is that prayers offered up in Jesus name connect directly to God. As we noted earlier, unbelievers who pray may only pray out of fear or out of need. Whenever a person is born again in saving faith, a new impulse is gained - namely the desire to desire God.
In the faithwalk with Jesus Christ, the need for God is sought first in order to better understand how to pray for other needs. Additionally, in one's faithwalk with Jesus Christ, fearing God means hating sin and seeking Him at all costs, thus transforming the basis for prayer from fear to faith (see Hebrews 11:1,6).
To know God and to enjoy Him can only occur when a person by grace through faith has trusted in Jesus Christ (Jeremiah 9:23-24; 2 Corinthians 5:15-21; 1 Timothy 2:5; Jude 1:20-25). In other words, only within a relationship with Jesus Christ by faith are prayers accepted by God, meaning that He commits Himself in covenant relationship to the Christian who prays in the name of Jesus (see John 9:31; Hebrews 4:13-16).
Moreover, unlike other religions, the Gospel and Biblical Christianity alone teach that Christians are able to pray in expectation of an answer due to the personal inner working of the Holy Spirit in their lives (Jude 20-23).
The cycle of how God works in the prayer-life of the Christian
If we were to summarize what makes prayer unique in relationship with Jesus Christ, it would be this: God commits Himself to pray in and through the Christian. In other words, the Holy Spirit initiates the promptings of prayer in the Christian's heart, resulting in a prayer offered up to the Father through the Son (Ephesians 2:18; Romans 8:26-27). The Son in turn takes every prayer received and intercedes on behalf of the Christian to the Father (1 John 2:1-2). Then thirdly, the Father responds by excercising His will through the continuing work of the Holy Spirit (Jude 1:20-23). If we can think of this "prayer-cycle" as the Triune God's involvement in the Christian's prayer life, no other religion comes even close to this supernatural, empowered reality of prayer.
In short, every other religion has people trying to reach up to God that they cannot know personally by religion or reason. Only by grace through faith alone in Jesus Christ does God reach down to make Himself known and commits Himself to the continual activity of doing so in the life of the believer. This is why we need Jesus Christ and the Holy Spirit for effective prayer.