Hebrews 11:1 defines faith, saying, "Now faith is the substance of things hoped for, the evidence of things not seen." The passage proceeds to cite Scriptural accounts of instances of faith.
I. The Faith which is enjoined in the Scripture is confidence in the word of the Lord God. The Scripture repeatedly cites the faith of Abraham as the exemplar of faith. Not until Abraham and Sarah were hopelessly past the physiological point of reproductive ability, did the Lord God promise Abraham that his seed would be in number as the stars of the heaven, Genesis 15:1-6. Abraham had confidence in the promise of the Lord God, and for that reason the Lord reckoned Abraham righteous.
It is the good pleasure of the Lord God to grant justification to those who place confidence in his word. And to place confidence in the word of the Lord is to place confidence in the Lord himself; consider Psalm 138:2. Abraham was justified, not because he "accepted Jesus as his personal saviour," but, rather, because Abraham had confidence in the promise of the Lord regarding progeny.
Consider Hebrews 11:6, which explains, "But without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him."
The one who diligently seeks the Lord is led by the Lord to the Scripture, from which he learns how to enter the Way of Life. Once in the Way, he seeks the Lord through the pursuit of sanctification. If he persists in the Way, he shall be born again, by the Resurrection, becoming a member of the family of God -- one of many Sons, Hebrews 2:10-13. The Lord does not welcome into his family any save those who trust him and diligently pursue relationship with him.
Our understanding of the Scripture has been impeded greatly by the slipshod contemporary usage of the English words faith, hope, and belief. Faith is not unfounded expectation that somehow something shall come to pass. Hope is not desire. Belief is not notion based on hearsay. In actuality, faith, hope, and belief are synonymous with confidence and trust; each of these words has the same essential meaning, namely, expectation founded upon a trustworthy basis.
The promises and declarations of the Lord are sure. The Lord God has the ability to do all that he has said that he shall do, and the Lord is faithful to his word. Accordingly, faith is an attitude of mind or certainty which views as tantamount to reality that which is promised by the Lord God. Consider Romans 4:17, "(As it is written, I have made thee a father of many nations,) before him whom he believed, even God, who quickeneth the dead, and calleth those things which be not as though they were."
And, indeed, the things promised which lie in the future, though not yet extant, together with the things of the Realm of the Spirit, though invisible, have a reality which transcends that of the things of the Natural Realm which are extant, visible, and tangible. Consider Hebrews 11:3, "Through faith we understand that the worlds were framed by the word of God, so that things which are seen were not made of things which do appear," and II Corinthians 4:18, "While we look not at the things which are seen, but at the things which are not seen: for the things which are seen are temporal; but the things which are not seen are eternal."
II. All that said, there are degrees of faith. The faith of some is strong; the faith of some is weak. The stronger the faith, the greater the accomplishment possible in the exercise of faith; consider Matthew 9:27-31, Mark 9:17-29, Matthew 6:24-34, Matthew 8:23-27, Matthew 14:24-32, Matthew 16:5-11, Matthew 17:14-21, Matthew 21:21, Luke 12:15-34. Romans 4:17-21, I Corinthians 13:2.