There is a providence; there is a God," said Monte Cristo, "of whom you are a striking proof, as you lie in utter despair, denying him, while I stand before you, rich, happy, safe and entreating that God in whom you endeavor not to believe, while in your heart you still believe in him.

This is a bit more of a literary studies question, though I suppose the usage is sufficiently obscure to have confused you. Providence is mentioned many times in The Count of Monte Crisco but is not a god, but an expression of God's will or plan, especially when it protects, benefits or provides for others. It is a reference to the doctrine of Divine Providence in Christian theology, an expression of God's omniscience and occasional intervention to see that the world continues according to plan - in this case, Dantes sees himself as an agent of Providence, an instrument of God's will. This is contrasted with blind fate, or a mechanistic, materialist universe where there is no moral dimension to events. In a sense, it acts to show Dantes' hubris by presuming to know God's will - the latter being a fairly widespread theme in literature.