There are a few different reasons why bees will fan their wings. They may be regulating temperature and humidity in the hive.
On hot days you will see bees at the front entrance moving air through the hive and cooling things down. The hive in the video above had two full supers of nectar, the extra airflow from the fanning helps reduce the moisture content of the nectar and cure it into honey.
In other instances they may fan their wings to help broadcast the nasonov pheromone. A few of the bees with their nasonov gland exposed are identified in this photo:
Bees stick their butts in the air and bend the last segment of their abdomen down to expose the gland. Here's a video of the same hive as in the photo above. See how many bees you can spot sending out the pheromone.
In this case the fanning bees are calling back a large group of bees that had been shaken out of the hive during an inspection. Similar behaviour occurs at a hive entrance when a swarm first reaches a new home, after orientation flights, or when a queen departs on a mating flight. A few more details about the nasonov gland can be found here.
Right away we noticed a few indications that led us to believe the swarm was queenless:
There was no single cluster. Bees were on the ground in two different locations and there were a few up in a tree.
The bees were spread out and fanning. While it was hot, it's likely they were searching for queen scent rather than trying to keep cool. Even once we got them into a nuc box they spread out over the available surface of the box rather than clustering.
They became very interested in the bee gloves of my friend John and actually started running en masse towards him when he first started looking for a queen.(You can see this in the video. Unfortunetly it's a little obscured as some bees had also become very interested in my camera at the same time.) I don't expect the residual bee smells on the gloves and camera would have been nearly as interesting if they had a queen giving them the pheremones they were really after.
We collected the bees and joined them with one of our weaker colonies. The colony we joined it with was a split with an old queen removed from a hive that had supersedure cells. We placed the swarm on top in a seperate box with a sheet of newspaper inbetween. Five days later we opened the hive to discover: the bees had already eaten two holes through the paper, one dead queen being mobbed by bees and one healthy looking queen going about her business.
We couldn't believe it. We searched for other explanations. Is it possible a virgin queen drifted back to the wrong hive from the other half of the split? Seems unlikely. So maybe the swarm did have a queen afterall. Upon reviewing the video again, I noticed relatively few bees fanning at the begining as compared with the end when some bees were already placed in a nuc box. Perhaps that should have been seen as sign the bees were just trying to keep cool vs. actually wondering about the current location of their queen?
Lesson? Check and double check when there is any doubt about a queens existence.