And in that day ye shall ask me nothing. Verily, verily, I say unto you, Whatsoever ye shall ask the Father in my name, he will give [it] you.
Note 87 at Joh 16:23: Ever since sin entered the world, man has always had to go through some mediator to approach God. This was because of God's holiness and man's sinfulness. In the Old Testament, sacrifices and priests were symbolic mediators. In the New Testament, Jesus is our High Priest mediator (Heb 3:1 and 9:15).
However, Jesus' mediation was greater than anything that had ever existed before in that He not only was pure but also actually cleansed and purified the ones whom He was representing. Now we can come directly to the Father in His name. This is what Jesus was referring to, and it was a radical statement to the disciples.
It is awesome to think that we can commune directly with Almighty God, the creator of heaven and earth, but that is exactly what Jesus provided for. In Joh 16:26-27, Jesus revealed that He had reconciled man to God so completely that the disciples wouldn't have to pray to Him and then have Him relay the message to the Father, but they could go directly to the Father Himself.