Now faith is the substance of things hoped for, and the sign that the things not seen are true.I think the key words are assurance, being sure, confidence, conviction, certainty. If this is what faith is in the biblical sense--being sure of receiving/attaining things that one hopes for, being sure of the reality of things one does not and cannot see (perceive)--then it is quite synonymous with how we usually understand "faith," i.e., a firm belief without evidence or strong belief despite the lack of evidence.
Now faith is the assurance of things hoped for, the conviction of things not seen.
Faith assures us of things we expect and convinces us of the existence of things we cannot see.
Faith is a sure confidence of things which are hoped for, and a certainty of things which are not seen.
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.
And faith is of things hoped for a confidence, of matters not seen a conviction,
Now faith is being sure of what we hope for, being convinced of what we do not see.
Now faith is being sure of what we hope for and certain of what we do not see.
What is faith? It is the confident assurance that what we hope for is going to happen. It is the evidence of things we cannot yet see.
The fundamental fact of existence is that this trust in God, this faith, is the firm foundation under everything that makes life worth living. It's our handle on what we can't see.
Immediately, however, as with believing in any other thing Hebrews 11:1 runs afoul of epistemology. However sure, confident, and certain we are that what we hope for and what we cannot see is true, our fervent belief tells us nothing about whether in fact we are right or wrong, whether or not what we believe in is true/real. For example, there are adherents of every religion who are die-hard believers. But since many claims of the various religions of the world conflict with one another and therefore cannot be true simultaneously, then clearly faith (belief) does not lead to (an apprehension of) the truth. Surety, confidence, certainty are just that. They do not imply that what is believed in is true, much less make it true.
Given that they planned and trained for years with the ultimate goal of sacrificing their lives, the 9-11 terrorists must be counted among those who had the most faith in their beliefs. However, it's rather comical to conclude that simply because these hijackers firmly believed their deity would reward them with six dozen virgins each for their murderous deeds, they in fact are now wallowing in a sea of young females in some dimension.
So faith is irrelevant to the truth of the belief. But Christians believe in Hebrews 11:1. And some believe in it with all their hearts. But as we have already said believing will not suddenly make that which is believed in true. Merely believing in Hebrews 11:1 or being certain (having faith) that the claim therein is true does not tell us anything about the truth of that passage. The pertinent question for Christians therefore is: Why do you believe that verse? Why do you believe the claims therein? What makes you sure that it is true? Queried, they will almost surely whip out some lame reason (e.g. "because it's in the bible," "because it's God's word") which does not at all justify the belief, or which contains implicit premises that have not been substantiated and known to be true, or which ultimately ends up begging the question (circular reasoning).
I am led to hypothesize that believers are not truth seekers at all. "The truth will set you free" is paid lip service. Instead believers are in the business of taking as truth that which they want to be true and that which they hope for (remember, they cherry pick) regardless of whether or not these beliefs are rooted in reality, plausibility, and rationality. In effect they unconsciously tell themselves: "I like the idea of an afterlife, of spending an eternity with my loved ones, therefore I will hold this belief despite and regardless of ...." "I feel solace and comfort in the idea of a benevolent deity who hears and answers prayers therefore I will continue to believe in it despite and regardless of ...." Preference trumps evidence and rationality. And there's an obstinacy and hard-headedness to it that appropriately deserves the epithet "blind faith." Believers seem to be declaring: I believe this to be true and real whether or not it is true and real.
Faithing in contrast to thinking seems to be prime mover amongst Christians. As the Apostle's creed epitomizes there's an emphasis on believing. Believe and you will be saved. Believe and you will be healed. Just believe. And when Christians run into disconfirming evidence and cognitive dissonance, they just go over the bumps, forget about it in no time, and move on, their belief engine chugging along as if nothing had happened.
It seems to me in order to arrest this runaway train takes a mountain of cognitive dissonance, something their faith can't move or go over or around. But what will actually break the spell (not exactly as Dan Dennett used the phrase) is idiosyncratic for every believer, as stories of deconversion show.