It is like a dog's pant, but it definitely means they need some help cooling off.
I just discovered a new way to help my birds in the heat. The tarp I had over part of the run had been shredded by the squirrels over the winter and I have used an old king sized bed sheet folded in half and some clothes pins to replace it until I buy another tarp. Today when I went to hook up my mist system to the hose it broke right at the hose connection spot. It is 105 right now and I knew I needed to cool my adults off. They are in a section of the run where the sheet is. So I first misted them with a spray nozzle, but then I decided to spray the coop and trees above the run too. In the process I wet the sheet. It is now dripping into the run like the ending of a nice spring shower. So, if you can't get a mister and you have a run covered with wire, a bed sheet and the hose will work until you can do something else.
Another idea for those using fans is to place some of the frozen bottles right behind the fan so that it is drawing cooler air through.