Thankfully, the Bible contains a clear definition of faith in Hebrews 11:1: “Now faith is the assurance of things hoped for, the conviction of things not seen.” Simply put, the biblical definition of faith is “trusting in something you cannot explicitly prove.”
This definition of faith contains two aspects: intellectual assent and trust. Intellectual assent is believing something to be true. Trust is actually relying on the fact that the something is true. A chair is often used to help illustrate this. Intellectual assent is recognizing that a chair is a chair and agreeing that it is designed to support a person who sits on it. Trust is actually sitting in the chair.
Understanding these two aspects of faith is crucial. Many people believe certain facts about Jesus Christ. Many people will intellectually agree with the facts the Bible declares about Jesus. But knowing those facts to be true is not what the Bible means by “faith.” The biblical definition of faith requires intellectual assent to the facts and trust in the facts.
Believing that Jesus is God incarnate who died on the cross to pay the penalty for our sins and was resurrected is not enough. Even the demons believe in God and in those facts (cf. James 2:19). We must personally and fully rely on the death of Christ as the atoning sacrifice for our sins. We must “sit in the chair” of the salvation that Jesus Christ has provided. This is saving faith. The faith God requires of us for salvation is belief in what the Bible says about who Jesus is and what He accomplished and fully trusting in Jesus for that salvation (Acts 16:31). Biblical faith is always accompanied by repentance of sin (Matthew 21:32; Mark 1:15).
The biblical definition of faith does not apply only to salvation. It is equally applicable to the rest of the Christian life. We are to believe what the Bible says, and we are to obey it. We are to believe the promises of God, and we are to live accordingly. We are to agree with the truth of God’s Word, and we are to allow ourselves to be transformed by it (Romans 12:2).
Why is this definition of faith so important? Why must trust accompany agreeing with facts? Because “without faith, it is impossible to please God” (Hebrews 11:6). Without faith, we cannot be saved (John 3:16). Without faith, the Christian life cannot be what God intends it to be (John 10:10).
 Got Questions Ministries. (2010). Got Questions? Bible Questions Answered. Bellingham, WA: Logos Bible Software.