"Whereof the Holy Ghost also is a witness to us: for after that he had said before," (Hebrews 10: 15)
When we learn about the Holy Spirit, we learn about the gift tongues, miracles, and other supernatural, manifested works.
When Jesus taught His disciples about the Holy Spirit, He described Him as our Paraclete, or our comforter, our advocate:
"But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me:" (John 15: 26)
The writer of Hebrews declares that the Holy Spirit is our witness, for He witnesses of Jesus.
The Amplified Bible expounds on the term Paraclete:
"But when the Comforter (Counselor, Helper, Advocate, Intercessor, Strengthener, Standby) comes, Whom I will send to you from the Father, the Spirit of Truth Who comes (proceeds) from the Father, He [Himself] will testify regarding Me." (John 15: 26, AMP)
The Holy Spirit is our counselor:
"20But ye have an unction from the Holy One, and ye know all things." (1 John 2: 20)
"But the anointing which ye have received of him abideth in you, and ye need not that any man teach you: but as the same anointing teacheth you of all things, and is truth, and is no lie, and even as it hath taught you, ye shall abide in him." (1 John 2: 27)
He is our helper, when we do not know what to pray:
"Likewise the Spirit also helpeth our infirmities: for we know not what we should pray for as we ought: but the Spirit itself maketh intercession for us with groanings which cannot be uttered." (Romans 8: 26)
He is our intercessor, speaking on our behalf through Christ Jesus our High Priest:
"And he that searcheth the hearts knoweth what is the mind of the Spirit, because he maketh intercession for the saints according to the will of God." (Romans 8: 27)
He also strengthens us, as we pray in the Spirit:
"He that speaketh in an unknown tongue edifieth himself; but he that prophesieth edifieth the church." (1 Corinthians 14: 4)
Because of the Holy Spirit, we also know that He will never leave us nor forsake us.
"5Let your conversation be without covetousness; and be content with such things as ye have: for he hath said, I will never leave thee, nor forsake thee." (Hebrews 13: 5)
In the context of the above verse, the Holy Spirit witnesses to us the full contents of the New Covenant.
The Holy Spirit today is our witness of Jesus, and He is our Paraclete, an all-encompassing aid for all things.