To believe, St. Augustine tells us, is to think with assent.
St. Thomas unpacks this definition somewhat, explaining that the kind of thinking involved in belief is what happens when you're deliberating over the truth of something but have not yet reached the "certitude of sight."
As the act of faith, belief is an action, a movement of the mind toward certitude. What makes belief a unique action of the mind is that it is a deliberation toward an answer we already assent to. Fr. Walter Farrell, OP, puts it this way:
It is, of course, paradoxical that our intellect should be restless, pondering, in the face of a truth, yet at the same time assent to that truth firmly. Actually this definition brings out the full nature of the act of faith. We do not suspect this truth, as a man might suspect the presence of burglars from the uneasiness of his dog; we are not doubting it; we have not merely an opinion of it, such as we might gather from the hasty accounts in a morning newspaper; we do not see it clearly, as we might the results of a scientific experiment. We believe it. And we thereby produce an act distinct from all other acts of the mind.