To pray in Jesus’ name means to offer prayer to God the Father through the ministry and work of Jesus.  It implies that the person who is praying in Jesus’ name has received Christ as Savior (John 1:12) and has been justified by faith (Romans 3:28; 5:1).  This means he is a new creature (2 Corinthians 5:17), indwelt by God (John 14:23), who is born again.  Therefore, he has the right to pray to God through Jesus who lived a perfect life (1 Peter 2:22) and bore our sin in his body on the cross (1 Peter 2:24).  It is also a designation of authority because Jesus has the authority to go to God the Father, and we who are in Christ (1 Corinthians 15:22) also have been given that same authority.  This is why people will often end their prayers by saying “in Jesus’ name, amen.”  What they are intending to do is address God the Father through Jesus, by depending completely on his work and perfection since he is, after all, God in flesh (John 1:1, 14; Colossians 2:9).

John 14:13–14, “Whatever you ask in My name, that will I do, so that the Father may be glorified in the Son. 14 If you ask Me anything in My name, I will do it.”

Furthermore, the phrase “in Jesus’ name” designates authority.  In Acts 4:7, 10 we see religious leaders asking Peter by what authority he healed a sick man.

Acts 4:7, 10, And when they had placed them in the center, they began to inquire, “By what power, or in what name, have you done this?”…10 “let it be known to all of you, and to all the people of Israel, that by the name of Jesus Christ the Nazarene, whom you crucified, whom God raised from the dead—by this name this man stands here before you in good health.”

So, it should be obvious that “in Jesus’ name” is a phrase that designates authority, and when we pray in his name we are praying in his authority because we have trusted completely what Christ has done on the cross to forgive us of our sins.