What is biblical faith?
Faith is the substance of things hoped for, the evidence of things not seen. Hebrews 11:1
Faith makes what you know to be a possibility clear as reality/substance. You cannot truly hope for something that you do not know to be a possibility. No one can truly hope to see a purple unicorn standing in front of their house. It isn’t a possibility, therefore you cannot believe you will see a purple unicorn. Faith is the evidence for what you have reasoned or hoped for (I am not using reason and hope as synonymous). Faith settles the argument. This is why new believers talk about the change in their mindset when they receive faith–things become clearer to them as a believer. Faith settles the argument they had been having within themselves about what is true or simply a possibility.
Biblical faith is a gift and should not be confused with the idea of mustering up trust in something (Ephesians 2:8). It is what makes spiritually blind people see (And has made physically blind people see). Biblical faith is received, not found within the natural man according to 2 Peter 1:1. Faith is a new set of eyes/lenses to see with. It is proof positive vision of what has been reasoned to be a possibility. There is no one who does not reason that the Christian worldview is a possibility because of general revelation (Romans 1, Psalm 19). In other words faith, as a gift from God, is a means provided by God to perceive the proof.
Now without faith it is impossible to please God, since the one who draws near to him must believe that he exists and that he rewards those who seek him. Hebrews 11:6
How does this verse distinguish secular faith from biblical faith? What kinds of things please God? We could make a long list of which many things on the list can be performed by unbelievers. Whether they choose to perform these acts because of cultural norms or the position of utilitarianism–they nonetheless do things that God considers good. However, he is not pleased with these actions unless the individuals “believe” that he exists and they draw near to him because of biblical faith. He doesn’t reward mere good acts. He rewards those who do it for his glory. He rewards those who diligently seek him in other words. This is a good place to make the biblical distinction between the concept of receiving faith from God as a gift, and trusting in him as the one who declares what is right and wrong, true or false. When one receives faith, based on that faith alone, they can then trust God, his Word, and his Spirit that teaches us things we do not know.