Hi Melissa,
The timer itself incorporates a small electric motor that's responsible for rotating the dial at a very slow rate, something on the order of 1/60th RPM, meaning it takes an hour to make a single rotation.
My son's washer died in exactly the same way; everything worked but the timer wouldn't advance. Taking it apart and powering the motor separately, I found that it wasn't turning at all. Unfortunately, on his washer the motor wasn't available separately so I had to replace the entire timer assembly when the problem was only the motor; I have no idea whether yours will be the same situation or not.
If you'd like specific information about replacement parts and/or repair instructions, we'd need to know the model number of your washer.