What does it mean to pray in Jesus' Name? A few times in the book of John, Jesus instructs us to pray "in His Name".  What does this mean?  How do we know if we are praying in His name?  How would we not be praying in His name?

I don't believe this is using "In Jesus' Name, Amen" as the closing line of our prayers.


  Whatever you ask in my name, this I will do, that the Father may
  be glorified in the Son.  If you ask me anything in my name, I
  will do it.  John 14:13-14 ESV
  
  You did not choose me, but I chose you and appointed you that you
  should go and bear fruit and that your fruit should abide, so that
  whatever you ask the Father in my name, he may give it to you.  John
  15:16 ESV
  
  In that day you will ask nothing of me. Truly, truly, I say to you,
  whatever you ask of the Father in my name, he will give it to you.
  Until now you have asked nothing in my name. Ask, and you will
  receive, that your joy may be full.  "I have said these things to you
  in figures of speech. The hour is coming when I will no longer speak
  to you in figures of speech but will tell you plainly about the
  Father. In that day you will ask in my name, and I do not say to
  you that I will ask the Father on your behalf; for the Father himself
  loves you, because you have loved me and have believed that I came
  from God.  John 16:23-27 ESV


Interestingly, there are other things that refer to "in Jesus' name':


  Whoever receives one such child in my name receives me  Matthew 18:5
  ESV
  
  For where two or three are gathered in my name, there am I among them.
  Matthew 18:20 ESV
  
  Many will come in my name, saying, 'I am he!' and they will lead many
  astray.  Mark 13:6 ESV
This can be answered by answering a more general question: what does "in someone's (anyone's) name" mean?  It means to act by proxy, on the authority of something or someone greater than yourself. It's a concept that our culture has kind of lost, though it still exists as a storytelling trope.  When a medieval herald reads a proclamation "in the name of the king," or a cop yells at a fleeing thief to "stop in the name of the law!" this is what they mean.  It's a convenient shorthand for "I'm not just saying this of myself; I'm speaking with the authority of a higher power."

So how does this apply to acting (and praying) in the name of Christ?  It means to act in his place.  To pray in the name of Jesus is to pray what Jesus would pray if he were in your position.  When we understand this in the context of Christ as the Perfect Man and our Exemplar, it means to pray for the right things, to seek the will of God and not our own desires.  And whatever we ask the Father in the name of Jesus Christ, that will be given to us.