In short: the unfolded state is a high-energy state of the protein, which will move towards lower-energy states. Some of these states are the folded protein, while others states are denatured protein (forming "wrong" interactions with itself or other proteins). Energy barriers between these states keep the protein in the denatured state even though the folded state might me more favorable.
Or in other words: it's trapped in the denatured state because of kinetics, even though thermodynamics would favor the folded state.
A nice figure to illustrate this: http://www.ghrnet.org/index.php/jbmbr/article/viewFile/1027/1397/6798