A vented gas fireplace is where you have a fireplace that is vented to the outside. This fireplace is generally safer and can be run for long periods of time without causing your room to be too hot. This is the most common type of gas fireplace int he Denver area.
A fireplace that is not vented means the air that it consumes comes from the room where the fireplace is situated. In addition, none of the heat it produces escapes to the outside. This type of fireplace produces a ton of heat and has to be cycled on and off throughout the day.