The Book of Hebrews gives us a very basic definition of faith.
1. Now faith is the substance of things hoped for, and the conviction of things not seen. (Hebrews 11:1)
Why is faith in God so important to the life of a believer? It is because without it NO ONE can please the Eternal. It is necessary for those who come to the great God to have faith he not only exists but that he will reward those who dilegently look for him (Hebrews 11:6).
What did faith motivate people in the Bible to do? According to the apostle Paul in the book of Hebrews, it moved Noah to build the ark even though it would be needed one hundred and twenty years after its construction started. As a result of his actions God considered him righteous (Hebrews 11:7).
8. By faith Abraham, being called of God to go out into the place which he would later receive for an inheritance, obeyed and went, not knowing where he was going.
11. By faith also Sarah herself received power to conceive seed, and gave birth when she was well beyond the childbearing age