What is the Holy Spirit?
The Holy Spirit, or Holy Ghost, is the third member of the Godhead.
The Holy Ghost is a personage of spirit. He is referred to in the the scriptures often as the Comforter, Holy Spirit or the Spirit of God. For example, shortly before Jesus’ crucifixion, He assured his disciples that he would not leave them comfortless.
But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
~ John 14: 26
The role and mission of the Holy Spirit is to testify of truth, particularly that God is our Heavenly Father and that Jesus Christ is our Savior.
Those who are baptized by proper priesthood authority may receive the Gift of the Holy Ghost, which is the right to have the constant guidance and companionship of the Holy Spirit when one is worthy.
Aside from the Bible, the Holy Ghost and the nature of the Godhead is spoken of in other books of scripture read by Mormons. For example, in the Doctrine and Covenants, we read:
The Father has a body of flesh and bones as tangible as man’s; the Son also; but the Holy Ghost has not a body of flesh and bones, but is a personage of Spirit. Were it not so, the Holy Ghost could not dwell in us.
~Doctrine & Covenants 130:22