When you say "ένα ποτήρι νερο" it means "a glass of water" but when you say "ένα ποτήρι του νερού" it means the glass that is used for drinking water, only the glass without the water. For example you can say "Πίνω 10 ποτήρια νερό κάθε μέρα" and also say "Ήπια 2 ποτήρια του νερού με κρασί". Is it clear to you?