What IS This "Holy Ghost"?

Read John Gill:
... he is a Person, and not a mere name and character, power or attribute of God; which will appear by observing,
1a. That the description of a Person agrees with him; that it subsists and lives of itself, is endowed with will and understanding, or is a willing and intelligent agent. Such is the Spirit of God; as the Father has life in himself, and the Son has life in himself, so has the Holy Spirit; since he is the author of natural and spiritual life in men; which he preserves unto eternal life; and therefore called, the Spirit of life; which he could not be, unless he had life in himself; and if he has life in himself, he must subsist of himself: he has a power of willing whatever he pleases: the apostle, speaking of his influences, administrations, and operations, says, “All these worketh the one and the self-same Spirit, dividing to every man severally as he will”, (1 Cor. 12:11) and that he is an intelligent agent, is clear from his knowing the things of God which none can know but him; and from his teaching men all things, and guiding them into all truth, and giving the spirit of wisdom and knowledge to one and another; now “he that teacheth men knowledge, shall not he know?” (1 Cor. 2:11, 12:8; John 14:26, 16:13; Ps. 94:10).
1b. Personal actions are ascribed unto him; he is said to be a reprover and convincer of men; to reprove or convince the world of sin, righteousness, and judgment (John 16:8). Now he that convinces another of his mistakes, brings him to a sense and acknowledgment of them, and to repentance for them, must be a Person, and not a mere name and character. He is spoken of as a teacher, that teaches all things, all doctrines necessary to salvation, and all the duties of religion: an human teacher is a person, and much more a divine one, (John 14:26; 1 John 2:27) he is promised as a Comforter, (John 16:7) and which he answers to, by shedding abroad the love of God in the hearts of the Lord’s people; 12:10; Rom. 8:26, 27). Now as the advocacy and intercession of Christ, prove him to be a Person, and a distinct one from the Father, with whom he intercedes; so the intercession of the Spirit, equally proves his personality, even his distinct personality also: to which may be added, that the Spirit is the giver of gifts to men, whereby they are qualified for the work of the ministry, (1 Cor. 12:8-11) and he calls them to that work, and appoints and sets them as overseers of particular churches, to feed them with knowledge and understanding, (Acts 13:2, 20:28)
1c. Personal affections are ascribed to the Spirit; as love, grief, &c. we read of the love of the Spirit, as well as of the Father, and of the Son; and which appears in the regeneration and sanctification of men, and in the application of grace unto them, (Rom. 15:30) and of the Spirit’s being grieved with the sins of God’s people, and their unbecoming behavior towards God and one another, (Eph. 4:30) and of his being rebelled against, vexed, and provoked; as he was by the Israelites (Isa. 63:10). All which could not be said of him, was he not a person. He is, moreover, said to be lied unto; as by Ananias and Sapphira, (Acts 5:3) and to be blasphemed, and sinned against with an unpardonable sin, (Matthew 12:32, 33)
2. Secondly, The Holy Spirit is not only a Person, but a distinct Person from the Father and the Son; and besides his distinctive relative property, spiration, or being the breath of them both, and so distinct from each; the following things may be observed:
2a. His procession from the Father and the Son: of his procession from the Father express mention is made in (John 15:26) and therefore must be distinct from the Father, from whom he proceeds; which, whether it respects his nature or his office, proves the same.
2b. The mission of the Holy Spirit, by the Father and the Son, clearly evinces his distinct personality from them; of his being sent by the Father, see (John 14:16, 26) and of his being sent by the Son .