The words, "by faith," are seen many times in Hebrews 11. Hebrews 10:38 says that the just shall live by faith, then chapter 11 gives examples of those who did, and the first few verses of chapter 12 admonish us to be faith people, also.
This section begins by talking about the faith of Moses' parents, as they hid for three months. The Bible says that they saw that he was a "goodly child." I would imagine that most parents thought their children were "goodly," but it is likely that God gave Zipporah, Moses' mother, some special insight concerning this child. We do not know what that might have been, exactly, but we do know that Bible faith is faith based on God's word, and the text says they hid Moses by faith.
Verse 24 begins to talk about Moses own personal faith. It was when he "had come to years." He was fully matured, and from other Scriptures, we know that he was 40 years old. He made some faith decisions: 1) he chose affliction over pleasure; 2) reproach over treasure; 3) the invisible God over the visible king; 4) and, he chose later of now. He belived his choices would yield a great reward. He was exactly right!
Now, here is the way the modern-day, lukewarm, affluent Christian mind would work, here is the kind of advice they would give: "Moses, it is true that the people of God are suffering great affliction, but God has placed you in a very strategic position to be able to relieve their suffering. You are one of the few people in the world who can walk right in and talk to Pharaoh. You eat at his table, and you are his step-grandson. You need to stay right where you are and use your influence to turn the heart of the king, so that he will be nice to the Hebrew people."
Now, what's wrong with that advice? Two things: 1) It was not what God was calling Moses to do; 2) and, that would never get God's people back to the land of Canaan, and it was necessary for them to get back.
In verse 28, we see that Moses, by faith, did exactly what God told him to do about the Passover. He placed in faith in what God said, and that's what he did, and that is what he led others to do. Isn't that exactly what God expects us to, also?
Here are three important observations concerning faith: 1) according to 1 John 5:4, faith is the victory that overcomes the world; 2) faith is the necessary element to receive anything from God; 3) faith is not always logical, but when it is based on God's word, it is always right.