Why is it important for living organisms to have a good temperature moderator such as water?

Because water does not gain or lose heat easily. If it did, we would undergo such large temperature swings that we would not be able to live. Further, the heat of evaporation for water cools a body, so not only does it keep the temperature constant, it also allows it to cool.

The bodies enzymes and proteins are very sensitive to body temperature. If the body temperature is not protected by a substance such was water when the temperature rises the proteins and enzymes will denature. Denature thus not function properly which can lead to many deleterious states of health.

Water has a high specifc heat, meaning it has a high resistant to changing temperatures. It is better to moderate temperature for organisms because it doesn't boil or freeze at medium temperatures and it doesn't fluctuate a lot.