The eleventh chapter of Hebrews, known as the great Hall of Fame of Faith reciting the faith and resulting action of many Old Testament heroes, begins with a description of what faith is.
First, we see that it is the "substance of things hoped for." Biblically, we know that the Christian "hope" is a hope so real it has substance in the present. None of the people of faith recited in this chapter actually saw the promises made to them come to fruition, but they so believed in them that they lived in the present as if the future were reality.
The word "substance" occurs only two other times in Hebrews. It is used to speak of Christ as the exact representation of God's essence and nature, "Who being the brightness of his glory, and the express image of his person |i.e., substance|" (Hebrews 1:3). It is also translated "confidence," "for we are made partakers of Christ, if we hold the beginning of our confidence stedfast unto the end" (Hebrews 3:14), and speaks of a deep assurance. Putting this all together, our text could then be rendered, "faith is the essence of our assurance of things yet in the future."
The word "evidence" could be translated "conviction," or even "proof." The word implies a logical, airtight argument. "All scripture is given by inspiration of God, and is profitable for doctrine, for reproof |same word as 'evidence'|, for correction, for instruction in righteousness" (2 Timothy 3:16). This sort of evidence is something we know to be true, something about which we have such conviction we act accordingly.
The first half of the verse brings a future truth down into the present; the second half commits our lives to that truth. JDM