The concluding statement of Hebrews 10 starts the following discussion of the nature of faith and of its fruits as called out by God’s revelation from its earliest time.

Hebrews 11 is an illustration of the God kind of faith.

The key is Heb 11:27 By faith he forsook Egypt, not fearing the wrath of the king; for he endured as seeing Him who is invisible. NKJV

Chapter 11 demonstrates the nature of the only kind of faith acceptable before God, a faith triumphant in the worst of situations.

Faith apprehends as a real fact what is not revealed to the senses. It rest on the fact, acts upon it and is upheld by it in the face of all that seems to contradict it.

Faith is to really see the truth.

Heb 11:2-3 For by it the elders obtained a good testimony. 3 By faith we understand that the worlds were framed by the word of God, so that the things which are seen were not made of things which are visible.

It is faith that believes in spiritual realities. VS.1 Now faith is the substance of things hoped for, the evidence of things not seen. NKJV

Heb 11:4 By faith Abel offered to God a more excellent sacrifice than Cain, through which he obtained witness that he was righteous, God testifying of his gifts; and through it he being dead still speaks. NKJV

Heb 11:5 By faith Enoch was taken away so that he did not see death, "and was not found, because God had taken him"; for before he was taken he had this testimony, that he pleased God. NKJV

Walk - (all) along, apace, behave (self), come, (on) continually, be conversant [well informed about or familar with], be eased, exercise (self), follow, forward, go (about, abroad, along, forward, on,, up and down), greater, grow, lead, march, move (self), needs, be at the point, quite, run (along), send, speedily, spread, still, surely, travel (-ler), walk (abroad, on, to and fro, up and down, to places), wander, wax, be weak.

Heb 11:6 But without faith it is impossible to please Him, for he who comes to God must believe that He is, and that He is a rewarder of those who diligently seek Him. NKJV

diligently seek- to search out, i.e. (figuratively) investigate, crave, demand, (by Hebraism) worship:

Acts 13:22 And when He had removed him, He raised up for them David as king, to whom also He gave testimony and said, 'I have found David the son of Jesse, a man after My own heart, who will do all My will.' NKJV Ps. 119:68

Heb 11:6 But without faith it is impossible to please Him, for he who comes to God must believe that He is, and that He is a rewarder of those who diligently seek Him. NKJV

Ps 119:68 You are good, and do good; Teach me Your statutes. NKJV

David’s testimony about God.

Heb 11:7 By faith Noah, being divinely warned of things not yet seen, moved with godly fear, prepared an ark for the saving of his household, by which he condemned the world and became heir of the righteousness which is according to faith. NKJV

Heb 11:11 By faith Sarah herself also received strength to conceive seed, and she bore a child when she was past the age, because she judged Him faithful who had promised. NKJV

Faith obeys His command.

Heb 11:8 By faith Abraham obeyed when he was called to go out to the place which he would receive as an inheritance. And he went out, not knowing where he was going. NKJV

Acts 13:22 And when He had removed him, He raised up for them David as king, to whom also He gave testimony and said, 'I have found David the son of Jesse, a man after My own heart, who will do all My will.' NKJV

Heb 11:13 These all died in faith, not having received the promises, but having seen them afar off were assured of them, embraced them and confessed that they were strangers and pilgrims on the earth. NKJV

Heb 11:39 And all these, having obtained a good testimony through faith, did not receive the promise.... NKJV

2 Cor 1:18-20 But as God is faithful, our word to you was not Yes and No. 19 For the Son of God, Jesus Christ, who was preached among you by us--by me, Silvanus, and Timothy--was not Yes and No, but in Him was Yes. 20 For all the promises of God in Him are Yes, and in Him Amen, to the glory of God through us [spoken by us]. NKJV

Heb 11:13 These all died in faith, not having received the promises, but having seen them afar off were assured of them, embraced them and confessed that they were strangers and pilgrims on the earth. NKJV

Heb 11:14-16 For those who say such things declare plainly that they seek a homeland. 15 And truly if they had called to mind that country from which they had come out, they would have had opportunity to return. 16 But now they desire a better, that is, a heavenly country. Therefore God is not ashamed to be called their God, for He has prepared a city for them. NKJV

Heb 13:13-14 Therefore let us go forth to Him, outside the camp, bearing His reproach. 14 For here we have no continuing city, but we seek the one to come. NKJV

Heb 11:17-19 By faith Abraham, when he was tested, offered up Isaac, and he who had received the promises offered up his only begotten son, 18 of whom it was said, "In Isaac your seed shall be called," 19 concluding that God was able to raise him up, even from the dead, from which he also received him in a figurative sense. NKJV

Heb 11:21 By faith Jacob, when he was dying, blessed each of the sons of Joseph, and worshiped, leaning on the top of his staff. NKJV

Heb 11:25-26 ... choosing rather to suffer affliction with the people of God than to enjoy the passing pleasures of sin, 26 esteeming the reproach of Christ greater riches than the treasures in Egypt; for he looked to the reward. NKJV

Heb 11:27 By faith he forsook Egypt, not fearing the wrath of the king; for he endured as seeing Him who is invisible. NKJV

Heb 11:33-35 ...who through faith subdued kingdoms, worked righteousness, obtained promises, stopped the mouths of lions, 34 quenched the violence of fire, escaped the edge of the sword, out of weakness were made strong, became valiant in battle, turned to flight the armies of the aliens. 35 Women received their dead raised to life again. And others were tortured, not accepting deliverance, that they might obtain a better resurrection. NKJV

2 Chron 16:9 For the eyes of the LORD run to and fro throughout the whole earth, to show Himself strong on behalf of those whose heart is loyal to Him. NKJV

Faith suffers for God.

Heb 11:24-26; 35-38 ...choosing rather to suffer affliction with the people of God than to enjoy the passing pleasures of sin, 26 esteeming the reproach of Christ greater riches than the treasures in Egypt; for he looked to the reward. 35 Women received their dead raised to life again. And others were tortured, not accepting deliverance, that they might obtain a better resurrection. 36 Still others had trial of mockings and scourgings, yes, and of chains and imprisonment. 37 They were stoned, they were sawn in two, were tempted, were slain with the sword. They wandered about in sheepskins and goatskins, being destitute, afflicted, tormented-- 38 of whom the world was not worthy. They wandered in deserts and mountains, in dens and caves of the earth. NKJV

Acts 7:54-60 When they heard these things they were cut to the heart, and they gnashed at him with their teeth. 55 But he, being full of the Holy Spirit, gazed into heaven and saw the glory of God, and Jesus standing at the right hand of God, 56 and said, "Look! I see the heavens opened and the Son of Man standing at the right hand of God!" 57 Then they cried out with a loud voice, stopped their ears, and ran at him with one accord; 58 and they cast him out of the city and stoned him. And the witnesses laid down their clothes at the feet of a young man named Saul. 59 And they stoned Stephen as he was calling on God and saying, "Lord Jesus, receive my spirit." 60 Then he knelt down and cried out with a loud voice, "Lord, do not charge them with this sin." And when he had said this, he fell asleep. NKJV

Heb 11:15-16 And truly if they had called to mind that country from which they had come out, they would have had opportunity to return. 16 But now they desire a better, that is, a heavenly country. Therefore God is not ashamed to be called their God, for He has prepared a city for them. NKJV