Water vapor will begin to buildup in the air in the covered glass.  Some of that water vapor will begin to condense.  The amount of water vapor will increase until the rates of condensation and evaporation become equal.  The water vapor concentration won't change after that.  The air is saturated with water vapor.

When air is saturated it is filled to capacity with water vapor.  The actual amount of water vapor will depend on the air's temperature, warm air can contain more water vapor than cold air can.