A clear understanding of faith in Hebrews 11 largely depends on how we perceive the word "substance" in verse 1. In Greek, it is hypostasis, literally "a standing under." A more complex definition is "that which underlies what is apparent." Amplified a bit further, it is that which, though unseen, exists beneath what is visible. It, then, has the sense of a foundation. Even as the foundation of a building is unseen, but the building above ground is apparent, the foundation, the hypostasis, is nonetheless real, supporting the building. Hypostasis is the unseen support of what is standing in clear view.
Spiritually, then, invisible faith underlies, supports, and thus motivates the visible action. However, that does not end the discussion of how hypostasis is to be understood. Should it be understood subjectively or objectively? In other words, should we consider faith to be a quality, a virtue within us (that is, subjectively), or should we understand it as something not a part of us but on which we can rely (that is, objectively)? Neither of these usages is wrong, but one seems better than the other within the context of the entire book.
If the translators believed it should be understood subjectively, then the first phrase in Hebrews 11:1 will be translated similar to, "Faith is being sure of what we hope for, certain of what we do not see." Another subjective variation might be, "In faith, things hoped for become a reality." This emphasizes conviction, an internal certainty about what we believe.
If the translators believed it should be understood objectively, then the same phrase will be translated, "Faith is the substance of things hoped for" or "Faith is the title deed of things hoped for." This emphasizes something outside the person that he can rely upon.
This issue is not an easy matter. However, the subjective perspective, conviction within us, is better, given the tenor of the entire epistle.
Certainly, Paul spends a great deal of time reminding the Hebrews of how great what they believe in is—that things pertaining to Christ are far better than anything ever before offered to mankind. This by itself would require an objective point of view. However, the real problem was within these Hebrews' hearts. Paul was exhorting people who were letting the things of God slip away from them through personal neglect. It was not that they did not have something to believe in, for the epistle clearly states they had formerly done much better. Rather, through their lack of conviction, and thus their neglectful personal application, they were slip-sliding away. The real issue is subjective.
Several times, Paul urges them to recall former days and recapture the bold confidence they once had. Thus, though neither of these approaches is wrong, the subjective perspective is better, meaning Hebrews 11:1 is better translated, "Faith is being sure of what we hope for, certain of what we do not see." The believer is convinced that the things he cannot see regarding God are real, and so, from that perspective, he will act in fullness of hope.
Many claim to believe God, but what influence does this belief have on their behavior? If it wields little or no influence, they are unconvinced people, people without conviction who are seeking only an intellectual righteousness. Such belief is without certainty, and so it lackadaisically, gradually retreats instead of going forward in growth. These Hebrews had become this way under the pressure of time and trial.