Jesus is talking about the Holy Ghost in John 14. The promise of the Father is the gift of the Holy Ghost. (John 14, Acts 2:33, 38-42)
Acts 2:4
And they were ALL FILLED with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance.
Acts 2:33
Therefore being by the right hand of God exalted, and having received of the Father the promise of the Holy Ghost, he hath shed forth this, which ye now see and hear.
Acts 2:38-39
Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call.
Jesus made reference to the above when He stated:
"If ye love me, keep my commandments.
And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;
Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you." John 14:15-17