(A) What it is not. It is not a bare acknowledgment that Christ is a Savior. There must be this acknowledgment, but that is not sufficient to justify. The devils acknowledged Christ's Godhead. "Jesus the Son of God." There may be an assent to divine truth, and yet no work of grace on the heart. Many assent in their judgements, that sin is an evil thing—but they go on in sin, whose corruptions are stronger than their convictions. Many assent that Christ is excellent; they cheapen the pearl—but do not buy.
(B) What justifying faith is. True justifying faith consists in three things:
(1:) Self-renunciation. Faith is going out of one's self, being taken off from our own merits, and seeing we have no righteousness of our own. "Not having my own righteousness." Self-righteousness is a broken reed, which the soul dares not lean on. Repentance and faith are both humbling graces; by repentance a man abhors himself; by faith he goes out of himself. As Israel in their wilderness march, behind them saw Pharaoh and his chariots pursuing, before them the Red Sea ready to devour; so the sinner behind sees God's justice pursuing him for sin, before, hell ready to devour him; and in this forlorn condition, he sees nothing in himself to help—but he must perish unless he can find help in another.
(2:) Reliance. The soul casts itself upon Jesus Christ; faith rests on Christ's person. Faith believes the promise; but that which faith rests upon in the promise—is the person of Christ: therefore the spouse is said to "lean upon her Beloved." Faith is described to be "believing on the name of the Son of God," namely, on his person. The promise is but the cabinet, Christ is the jewel in it which faith embraces. The promise is but the dish, Christ is the food in it which faith feeds on. Faith rests on Christ's person, "as he was crucified." It glories in the cross of Christ. Gal 6:14. To consider Christ crowned with all manner of excellencies, stirs up admiration and wonder; but Christ looked upon as bleeding and dying, is the proper object of our faith; it is called therefore "faith in his blood." Rom 3:25.
(3:) Appropriation, or applying Christ to ourselves. A medicine, though it be ever so sovereign, if not applied, will do no good. Though the plaster is made of Christ's own blood, it will not heal, unless applied by faith; the blood of God, without faith in God, will not save. This applying of Christ is called receiving him. John 1:12. The hand receiving gold, enriches. Just so, the hand of faith, receiving Christ's golden merits with salvation, enriches us.
Source: A Body of Divinity by Thomas Watson