What does Hebrews 11:7 mean?

Faith, according to the writer of Hebrews, is what gives us confidence in an unseen future (Hebrews 11:1). When we trust God, based on what we know of Him, we act according to His will. That is the "faith" which God commends, and which is required in order to please Him. Prior examples of this kind of faith were Abel and Enoch.

Noah, listed here, also exemplifies trusting obedience. God's communication with Noah was relatively detailed—he was told about the upcoming flood and how the ark would serve to rescue mankind (Genesis 6:13–18). All Noah had to do was obey, which he did (Genesis 6:22). Of course, Noah would have grappled with his own unanswered questions, which is what the writer means by referring to "events as yet unseen." At the time God gave His command for Noah to build the ark, Noah had never seen anything like the flood before. He could see no physical evidence that the flood was imminent. But Noah chose to trust God.

This trust, sufficient to produce obedience, is what the writer of Hebrews extolls as the "faith" we ought to live by. Noah's trust proved the wickedness of those who rejected God, and his obedience saved his family (Genesis 7:11–13, 22–23). Noah is also referred to here as an "heir of the righteousness that comes by faith." Obedience to God, in the book of Hebrews, is often tied to the concept of an "inheritance," usually meaning the victorious rewards God intends us to obtain by following His will (Hebrews 6:11–12). Noah's behavior should be contrasted with the actions of the nation of Israel as described earlier in the book of Hebrews (Hebrews 3:7–15).