The first recipients of Hebrews are in a bad situation. They are paying the price of following Jesus and the price of loving others: severe opposition (doesn't this show just how upside down the world is? Severe persecution is the price of love). The result is that some are being tempted to to drift away from Christ and his saving message. Conviction is being driven on to the rocks and constantly battered by the waves. We see the outcome in 12:3 they are growing weary and losing heart. The sense of joy, assurance and power from the Holy Spirit have ebbed away, and the lures of the world are seeming much more enticing: "just give up, come back and join the rest of us and live will be nice and easy again."

How do we cling on in such circumstances? The writer's answer is "by faith." Faith is a word with a low currency today. "People of faith" is used on the TV to simply mean "belonging to a world religion," a definition so broad as to make the word practically useless. When the Bible uses it, it means something much more precise: faith in God's promises, trust in God's revealed true truth, acting on the evidences of what God has done in the world and in our lives, putting all our eggs in one basket - namely believing with security that God is real and has sent his son to atone for our sins and bring us to God. That's Christian faith. It isn't vague, nebulous or intangible. It isn't wish fulfilment or make-believe. It isn't "If I can just kid my brain to believe something that isn't true then maybe some magic will happen." It is neither irrational nor a mere intellectual appreciation of some facts we find incontrovertible.

Faith is trusting God - in reality, not just in theory. We only experience faith as real and valuable when we actually act on it - and find God working as He promised. He is reliable. We only discover if a chair is reliable when we sit on it. Theoretical faith in a chair's ability to hold our weight isn't really faith at all. In fact saying "I believe that this chair will hold my weight comfortably but I would rather not sit in it" probably reveals a secret underlying non-faith.

Hebrews 11 is full of examples of people just like the recipients of the letter. People who experienced opposition, who would have found it easy to lose heart, but who nevertheless trusted and saw what God used that trust to produce. Try making a list of all the things that God did with faith, in spite of opposition.

The question that the chapter begs is "how do we increase in faith in the face of opposition?" The answer is 12:2-3:

Let us fix our eyes on Jesus, the author and perfecter or 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. Consider him who endured such opposition from sinful men, so that you won't grow weary and lose heart

Jesus is the author of our faith. It comes from him, it is a gift of God. He produces it, we don't have to work it up. So thank him that your trust in him is not something that has come from yourself, and that it sin't dependent on the sincerity with which you can believe at any given moment
Jesus is the perfecter of faith. He is the one who is giving saving faith and will do so till the end, when he completes the work he has begun in us. He is at work doing it to this day. So ask him for more of it
He endured (severe) temporary suffering for the prospect of eternal joy. This is only possible when the eternal joy is perceived to be of greater extent than the temporary suffering. Therefore faith is produced by dwelling extensively on the joy of the future glory that awaits believers in the presence of God. So delight yourself in the fact that the New Heavens and the New Earth are ahead, that God has an inheritance waiting for you and that it is infinitely, oppositely, greater than the sufferings you are going through that tempt you to give up