Some ways that this verse is translated.
NOW FAITH is the assurance (the confirmation, the title deed) of the things [we] hope for, being the proof of things [we] do not see and the conviction of their reality [faith perceiving as real fact what is not revealed to the senses]. (Amplified Bible)
Now faith is the substance of things hoped for, and the sign that the things not seen are true. (Bible in Basic English)
Faith makes us sure of what we hope for and gives us proof of what we cannot see. (Contemporary English Version)
Now faith is a well-grounded assurance of that for which we hope, and a conviction of the reality of things which we do not see. (Weymouth New Testament)
Faith is the confidence that what we hope for will actually happen; it gives us assurance about things we cannot see. (The New Living Translation)
Some wise words concerning this verse.
Faith is to see as substantial fact what is hoped for on the basis of taking God’s promises seriously. It is to be assured of it, and to be convinced that what God has declared will be, seeing it as proved because He said it, even when it has not yet come about and is invisible. Thus it is to accept it as proved, on the basis of His word. Faith underpins hope in respect to what God has promised. Hope looks at what is to come with confidence, faith is satisfied that it will be so. The one who believes is satisfied that God has some better thing for him which is at present unseeable. (Pett)
True faith takes hold of the Divine word; it is weak or strong, great or small, as it receives, keeps, and uses, the word of God. The source of weak faith is in the ignorance and slowness of the heart with reference to the Divine testimony. The strength of faith is the humility of a helpless and broken heart cleaving to the promise. (Sermon Bible Commentary)
Faith is the sixth sense. It makes us as sure of unseen or future things, which we know about only through the divine Word, as we are of things which we can see and touch. When we are aware of the reality of these things, we naturally take them into account when we act. (F. B. Meyer)
The beginning point of faith is believing in God’s character: He is who he says. The end point is believing in God’s promises: He will do what he says. When we believe that God will fulfill his promises even though we don’t see those promises materializing yet, we demonstrate true faith. (Life Application Study Bible)
If people have faith, it means they believe that things hoped for according to God’s promises will be achieved and that unseen powers of God are real. Those with faith look beyond what they see. They know that they cannot explain the existence of the world solely by reasoning from the things that can be seen (11:1-3). (Bridgeway Bible Commentary)
“Now faith is the substance of things hoped for, the evidence of things not seen.” This is not a definition, but shows us something of what faith does. It is that which, to the individual, gives solid substance to things hoped for. It is no mere fanciful imagination, but an honest trust in the living God, by which the things of God are made a definite, clear reality to the heart, and are thus recognized to be more truly substantial than all material substance-for the latter will pass away. Also it has that peculiar power of evidencing to us “things not seen.” Faith in the living God is not blind, but the actual opening of the eyes, accepting unquestionable evidence of the reality of unseen, spiritual things. (L. M. Grant)
This is not a definition of faith but a description of what faith does and how it works. True Bible faith is not blind optimism or a manufactured “hope-so” feeling. Neither is it an intellectual assent to a doctrine. It is certainly not believing in spite of evidence! That would be superstition.
True Bible faith is confident obedience to God’s Word in spite of circumstances and consequences.
Read that last sentence again and let it soak into your mind and heart.
This faith operates quite simply. God speaks and we hear His Word. We trust His Word and act on it no matter what the circumstances are or what the consequences may be. The circumstances may be impossible, and the consequences frightening and unknown; but we obey God’s Word just the same and believe Him to do what is right and what is best. (Wiersbe)
There is no better definition of this elusive word than verse 1: ‘Now faith is being sure of what we hope for and certain of what we do not see’. People often excuse themselves as not being able to believe, as if faith were a matter of genes. All human beings live by faith, not least in our technological age. What matters is where we place our trust, and on what grounds. (Hacking)
It is the “confident assurance” (the expression is used of a title deed that guarantees a future possession) that what is anticipated will be realized (11:1). Faith treats unseen things as realities, not mere wishes or hopes. Throughout this chapter the issue of faith hinges on believing in what is not seen or what is future. (Tyndale Concise Bible Commentary)
Other Scriptures about Faith
He replied, “Because you have so little faith. I tell you the truth, if you have faith as small as a mustard seed, you can say to this mountain, ‘Move from here to there’ and it will move. Nothing will be impossible for you. ” (Matt. 17:20)
Through him you believe in God, who raised him from the dead and glorified him, and so your faith and hope are in God. (1 Pet. 1:21)
But now faith, hope, love, abide these three; but the greatest of these is love. (1 Cor. 13:13)
We live by faith, not by sight. (2 Cor. 5:7)
For it is by grace you have been saved, through faith–and this not from yourselves, it is the gift of God… (Eph. 2:8)
Let us fix our eyes on Jesus, the author and perfecter of our faith, who for the joy set before him endured the cross, scorning its shame, and sat down at the right hand of the throne of God. (Heb. 12:2)
Consequently, faith comes from hearing the message, and the message is heard through the word of Christ. (Rom. 10:17)
Some quotes about faith.
Faith, as Paul saw it, was a living, flaming thing leading to surrender and obedience to the commandments of Christ. (A. W. Tozer)
Faith expects from God what is beyond all expectation. (Andrew Murray)
Faith is to believe what we do not see, and the reward of this faith is to see what we believe. (Augustine)
Faith is a living and unshakable confidence. a belief in God so assured that a man would die a thousand deaths for its sake. (Martin Luther)
Faith isn’t the ability to believe long and far into the misty future. It’s simply taking God at His Word and taking the next step. (Joni Erickson Tada)
The beginning of anxiety is the end of faith, and the beginning of true faith is the end of anxiety. (George Mueller)
Where reason cannot wade there faith may swim. (Thomas Watson)
To one who has faith, no explanation is necessary. To one without faith, no explanation is possible. (St. Thomas Aquinas)
Faith is deliberate confidence in the character of God whose ways you may not understand at the time.(Oswald Chambers)
Never be afraid to trust an unknown future to a known God. (Corrie Ten Boom)
More quotes here. (I do not necessarily agree with all the teachings those quoted on this link.)