In animals symptoms are referred to as "clinical signs" or "signs". The clinical signs of diabetes are a result of high blood glucose concentrations.
Excessive blood glucose concentrations exceed the "glucose threshold" of the kidneys. When this happens glucose is excreted in the urine. This results in extra water loss from the body causing your diabetic dog to drink (and urinate) more.
Glucose, an important fuel (energy source), is being lost. So, a diabetic animal may eat more than normal but lose weight.
For more information on glucose metabolism see Canine diabetes.