The wetness on the grass in the early morning is dew. It is made up of droplets of water created by condensation and can also be found in the early evening.
When the temperature is low, the condensation becomes ice, and we know this as frost.
Dew, and indeed frost, look beautiful, especially in photographs. I particularly love to look at a spider web which is covered in frost or dew. It is easier to see and shows just how intricate they are.
Fun fact: Did you know that the Greek's had a Goddess of dew? Her name was Ersa!