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.
Dew will appear on thin objects that are exposed to the elements. What happens is that the object (grass, railings, leaves, etc.) radiate heat which then cools the surface. However, moisture in the atmosphere condenses faster than it can evaporate, and the result is water droplets - this is known as the dew point.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!