This is the closest thing we have to definition of faith in all the New Testament, I think. Now faith is the assurance of things hoped for, the conviction of things not seen. Here's how I would paraphrase this verse. Wherever there is full assurance of hope there is faith. Faith is the full assurance of hope.
Biblical faith is a confident expectation and desire for good things in the future.
But faith is more than that. By faith we understand that the world was created by the word of God. So faith is the larger idea. It includes hope, but is more than hope. Hope is faith in the future tense.