In Aquinas's commentary on Hebrews 11, Thomas has a nice way to pin down what the virtue of faith is, by distinguishing it from what it is not.
Because it is the substance of things hoped for, it is distinguished from faith or (as we might call it) belief in the ordinary sense. Ordinary belief is ordered to particular goods (whatever in the circumstances makes it good to believe); but the virtue of faith is ordered to our total and universal good, happiness.1
Because it is substance and evidence, it is distinguished from doubt, suspicion, and opinion. Those things do not involve firm adherence; the virtue of faith does.
Because it is evidence of things unseen, it is distinguished from knowledge and understanding, since what is known or understood in some sense is immediately apparent.
Therefore in the virtue of faith, intellect and will coincide in their object: Primary Truth and Ultimate Good recognized as one; understood in this way, it is a disposition or tendency toward complete happiness, total good; because this total good is not possessed, it tends toward it as hoped for and unseen. Thus, says Thomas, "faith is a habit of the mind by which eternal life is begun in us and that makes the intellect assent to things that it does not see."
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1 Incidentally, this is also why people who try to claim that Thomas's view of faith is wholly a matter of intellect just don't know their Aquinas.
