First, the opposite question: What isn’t faith?
Lots of people believe faith is necessary. What or whom your faith is in is less important to them that that you have faith. You might call this “faith in faith” or fideism. That’s not what Scripture calls faith. The object of faith is important. Just believing in a god doesn’t mean you believe in the one, true, Triune God.
Some people equate faith with feelings. If you have a positive feeling toward God, you can feel safe. This faith in feelings, or emotionalism, however, is not Biblical faith. Still others make faith into a work. God does the work of salvation except faith, which is the part you contribute. You put your faith in Him and endeavor to live a good life, and you can sleep comfortably at night. This notion of faith as a work is synergism, working together with God to accomplish salvation. But faith as God describes it, is the opposite of a work. (For a clearer understanding of these false notions of faith, see the chart “Saving Faith” on p. 2016 of The Lutheran Study Bible.)
Now to the question: what is faith? What does Scripture say? “For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast” (Ephesians 2:8-9). Faith is purely a gift from God, not a work. Belief in God does not come from within us, but from outside us: “Faith comes from hearing, and hearing through the word of Christ” (Romans 10:17).
Faith is perhaps best summarized with the Hebrew word “Amen.” Faith says “amen” or “yes” to God’s gifts. Faith says “amen” to God’s Word, His declaration that we are sinners, and His declaration that we are completely forgiven and covered in the righteousness of Jesus. Faith says “amen” to God’s Word, hearing it where and when it is preached. Faith says “amen” to God’s forgiveness, offered in His Sacraments. Faith says “amen” to God, receiving the gifts He bestows.
More than knowledge, more than belief that God exists, more than belief that Jesus died and rose, more than affiliation with other Christians, faith is full, complete, child-like trust in Jesus for forgiveness.
Faith is completely a gift. God gives it, guards it, grows it. What He gives is always enough.