If anyone knows how to tell us what faith is, it's Luther. This is from his introduction to his commentary on Romans.
"Faith is not what some people think it is. Their human dream is a delusion. Because they observe that faith is not followed by good works or a better life, they fall into error, even though they speak and hear much about faith. ``Faith is not enough,'' they say, ``You must do good works, you must be pious to be saved.'' They think that, when you hear the gospel, you start working, creating by your own strength a thankful heart which says, ``I believe.'' That is what they think true faith is. But, because this is a human idea, a dream, the heart never learns anything from it, so it does nothing and reform doesn't come from this `faith,' either. Instead, faith is God's work in us, that changes us and gives new birth from God. (John 1:13). It kills the Old Adam and makes us completely different people. It changes our hearts, our spirits, our thoughts and all our powers. It brings the Holy Spirit with it. Yes, it is a living, creative, active and powerful thing, this faith. Faith cannot help doing good works constantly. It doesn't stop to ask if good works ought to be done, but before anyone asks, it already has done them and continues to do them without ceasing. Anyone who does not do good works in this manner is an unbeliever. He stumbles around and looks for faith and good works, even though he does not know what faith or good works are. Yet he gossips and chatters about faith and good works with many words. Faith is a living, bold trust in God's grace, so certain of God's favor that it would risk death a thousand times trusting in it. Such confidence and knowledge of God's grace makes you happy, joyful and bold in your relationship to God and all creatures. The Holy Spirit makes this happen through faith. Because of it, you freely, willingly and joyfully do good to everyone, serve everyone, suffer all kinds of things, love and praise the God who has shown you such grace. Thus, it is just as impossible to separate faith and works as it is to separate heat and light from fire! Therefore, watch out for your own false ideas and guard against good-for-nothing gossips, who think they're smart enough to define faith and works, but really are the greatest of fools. Ask God to work faith in you, or you will remain forever without faith, no matter what you wish, say or can do. " (my italics)