According to Hebrews 11, faith is believing that God is, and trusting in what He has said. This kind of faith includes belief and also living according to that belief. It is demonstrated by obedience to God, and by continuing to believe His promises though we have yet to receive them.
Hebrews 11 is often referred to as the “Hall of Faith.” It includes people who lived by faith, and died in faith. The first inductee listed is Abel who by faith offered a more excellent sacrifice than his brother Cain (11:4). What made Abel’s sacrifice more acceptable than Cain’s was not the nature of his sacrifice, but the condition of his heart. Abel was a righteous man while Cain was dominated by sin (Gen.4). By faith we too can offer sacrifices well pleasing to God including the fruit of our lips which is giving praise and thanks to God (Heb.13:15), and doing good to others and sharing with them as they have need (13:16).