The liver acts as storage for glycogen (what glucose is called when it's stored). Cells within the pancreas produce two hormones: insulin and glucagon. Insulin is produced when our blood sugar is high. It works to lower blood glucose levels. The lower the blood sugar goes, the less insulin that's produced.
Glucagon is produced when blood sugar falls too low. It tries to normalize blood glucose by making the liver release its glycogen into the bloodstream, thus raising blood sugar levels. Liver enzymes can be tested to determine whether the liver is working properly.
Diabetics should strive to keep their blood sugar levels within normal range, that is between 70 mg/dl and 110 mg/dl. The exception is the 2 or 3 hours after eating. Then, ideally, blood sugar levels should remain below 180 mg/dl.