Hebrews 11:1

Now faith is the substance of things hoped for, the evidence of things not seen.
Faith - in its widest sense: not restricted to faith in the Gospel. Not a definition of faith in its whole nature, but a description of its characteristics in relation to Paul's exhortation to perseverance (Heb 10:39).
Substance ... - it substantiates God's promises, the fulfillment of which we hope for, making them present realities to us. [However, hupostasis is translated in Heb 3:14, 'confidence.'] So Alford. Thomas Magister, like our version, 'The whole thing is virtually contained in the first principle; now the first commencement of the things hoped for is in us through the assent of faith, which virtually contains all the things hoped for' (cf. note, Heb 6:5). Through faith, the future object of Christian hope, in in its beginning, is already substantiated (Heb 11:6). Hugo de Victor distinguished faith from hope. By faith we are sure of eternal things that they ARE; by hope we are confident that WE SHALL HAVE them. Hope presupposes faith (Rom 8:25).
Evidence, [elengchos] - 'demonstration:' convincing proof to the believer; the soul thereby seeing what the eye cannot see.
Things not seen - the whole invisible spiritual world. 'Eternal life is promised to us, but it is when we are dead; we are told of a blessed resurrection, but meanwhile we moulder in the dust; we are declared to be justified, and sin dwells in us; we hear that we are blessed, meantime we are overwhelmed in miseries; we are promised abundance of all goods, but we still endure hunger and thirst; God declares He will immediately come to our help, but He seems deaf to our cries. What should we do if we had not faith and hope to lean on, and if our mind did not emerge amidst the darkness above the world by the shining of the Word and Spirit of God?' (Calvin.) Faith is an assent unto truths credible upon the testimony of God (not on their intrinsic reasonableness), delivered unto us in the writings of the apostles and prophets. Christ's ascension is the cause; His absence the crown of our faith (Dr. Pearson). Faith believes what it sees not; for if thou seest, there is no faith, the Lord has gone away so as not to be seen: He is hidden, that He may be believed; the yearning desire by faith after Him who is unseen is the preparation of a heavenly mansion for us; when He shall be seen, it shall be given to us as the reward of faith (Augustine). As revelation deals with invisible things exclusively, faith is the faculty needed by us. By faith we venture our eternal interests on the bare Word of God: this is altogether reasonable.

(from Jamieson, Fausset, and Brown Commentary