Jesus is compacting a lot into the final hours of his ministry with the Twelve (minus one). I am certain there are books written at length discussing why He waited this long to get into these topics and I'm not going to try and equal those here. What we will look at is one portion, taken from John 16:7-8.
We need to look at who the "Counselor" is and what this means for us as Christians today. Let's tackle that in an exchange of affirmations and denials. This is a fairly common way to deal with theological issues, and it tends to give the boundary lines rather than all the shades of interior possibility. For simplicity sake, before we get started on that, please understand that I hold that the "Counselor" is the "Holy Spirit" (or "Holy Ghost," if you like the KJV, but that's a bad image for modern readers) and will just use "Counselor" since that's what is here.
First, this passage affirms that the Counselor is divine. Look on to 16:15 and see how the Counselor will take from what is Jesus' and tell it to the disciples. The only way for this is to work is for the Counselor to be capable of being with all the disciples at once--this requires omnipresence, the term we use to describe how God is always everywhere.
Second, this passage denies that the Counselor will bring anything that conflicts or overrides what is plain in Scripture. If the Bible is the Word of God, given in totality, then when the Counselor "speaks whatever He hears," He will be restating and reminding the listener of the Word of God.
Third, this passage affirms the primary mission of the Counselor is to illuminate the hearts of humanity to their need for a Savior. We see the truth about sin through the Counselor. We see how God will judge and what it is to be righteous through the Counselor. This passage does not address "spiritual gifts," which are spoken of in context of the church in later portions of the New Testament. Instead, the focus here is on how God works through the Counselor to bring people into a right understanding of who they are and who He is.
Fourth, this passage denies a heresy called "modalism." At times, people have looked at the Bible and believed that God is "God/YHWH" in the Old Testament, "Jesus" in the Gospels, and then the "Holy Spirit" after Jesus ascends. They tend to say that God shows Himself in three "manifestations" rather than always existing as three "persons," (think "something having personality"). But since we see here that Jesus is going to the Father, which means they exist simultaneously, and Jesus will send the Counselor, not become or transform into the Counselor.
Fifth, this passage affirms the need of believers for the Counselor. You will not figure it out on your own. You cannot. You need the presence of God to make life work.