diabetes

Increased hunger- cells say "look, we aren't getting any sugar, so feed us!"
They don't know that there already is a ton of sugar in the blood. They need the insulin to put the sugar inside, and if there is no insulin (or if the receptors that the insulin "fits" into is no longer accomidating to insulin), you STILL have hungry cells.
Increased thirst- dehydration occurs. You urinate constantly, so where are you getting that water? You are going to be thirsty all the time.
Glucose is kind of like salt. It draws water to it. Water loves to follow glucose and be next to it, as with salt. You only want a certain ratio of salt and glucose (and potassium, chloride, etc) per amount of water in your body. Your body does not want to fight with electrolytes and other things to pull water where it needs to be. It can't just take water and leave the salt there. You do use some basic principals in chemistry.
Increased urination- Well, if your body "sugar meter" says there is too much and wants to get rid of it, what's it supposed to do? So you can eliminate waste through urinating.

I hope this helped- I have to go~

This link explains the triad:

http://www.thedoctorsdoctor.com/diseases/diabetes.html

Another from eMedicine:

http://www.emedicinehealth.com/diabetes/page3_em.htm