What are some factors that drive the price of silver?

As you said, industrial supply/demand is the most important variable, but recently there has been something different going on and that is investment demand. With nearly every country having large deficits and debts, people are concerned with money printing and currency debasement which is driving up the demand for "hard" assets. Gold and Silver are the most tangible way to take advantage of this thinking as it is hard to store barrels of oil, or bales of cotton. Simplistically, I'd say people are using silver as a way to play currency debasement (declines in Dollar, Euro, Yen, etc).