“I will ask the Father, and He will give you another Helper, that He may be with you forever.” (John 14:16)

Jesus, knowing that His disciples were grieved by His impending departure from this world, comforts them with the promise of the Holy Spirit. In doing so, He also reveals an important truth about the Triune nature of God: 

First, Jesus promises them comfort through the Holy Spirit Who was coming. He said this Helper would “be with you forever.” He will not come and then have to leave, as Jesus did, but He would be with them as long as they live.  Indeed, Jesus’ promise to be with His disciples to the end of the age, and never to leave or forsake them, is fulfilled through the Holy Spirit. He is “God with us”; Jesus with His disciples always. He is truly the greatest comfort for the disciple.

But we also see the triune nature of God evidenced in this verse. We see three Persons involved in the sentence:
— “I”, Jesus
— “will ask the Father”, God the Father
— “and He will give you another Helper”, the Holy Spirit.

We see the distinctness of these personalities in the way Jesus describes that they relate to each other:
— Jesus is going to “ask” the Father. This is interaction between different Persons.
— The Father is going to “give” the Spirit — The Holy Spirit is Someone different than Himself or Jesus.

So we find here the presence of three distinct Persons, relating to each other. Yet as we know, there is but “one God” (Deut. 6:4). Hence the Tri-unity, “three in one” — the doctrine of the Trinity, taught here as well as throughout the New Testament.

But significantly, we find here that the doctrine of the Trinity is no mere “cold theological doctrine.” The Triune Persons of the Godhead are here represented as actively involved in bringing about the comfort of the disciples whom they love.