What exactly does the antidiuretic hormone have to do with urinary volume?

Reduces the volume.. Maintaining fluid balance is an important function of the body. When the body senses dehydration, the brain releases antidiuretic hormone (adh), also called vasopressin, to signal to the kidneys to conserve water. Reabsorption of water leads to lower urine volumes and more concentrated urine. Alcohol blocks ADH release, which is why you urinate so much after drinking.