You want to mark the queen bee so you can find her quickly if you need her replace her. Bees are very sensitive to temperature so its a bad idea to stand around for ages with their house open up. Marking her means that you probably wont have to spend ages searching for her should the need to replace her arise.
Find the lady. Finding a slightly larger queen amongst 30000 of her daughters while she tries to hide from the light can be tough.
Queens release pheremones (and queen substance) that signal her authority and generally keep the rest of the hive in line. These she secretes and produces from her mouth parts. Should these run low due to old age or various other reasons the hive stops being a well coordinated superorganism and turns into something like King Lear but with 30000 ungrateful daughters. Replacing her can stop this rebellion that can cause many of your bees to leave in a swarm.
Capturing the queen
Handling the queen can cause your odors to rub off on her. Then when she is added back to the colony she may not be recognised. This causes something similar to an immune response in the superorganism. If you later the odor of the queen badly she can be murdered by the colony. To avoid this some experiments with using gloves are taking place.
In this case the gloves are odorless polythene similar to the ones used at sandwich counters. Unfortunately they are too baggy and so John said he would not use them again.
The queen is having her wings clipped here. Occasionally the when the queen is not producing enough queen substance to keep the colony from rebelling she will attempt to flee with some of the hive. If this happens you can lose half of your hive. If she does leave with clipped her wings shell fall to the ground and those bees who were leaving with her should head back to the hive. Dealing with swarming is a large area.
Marking the queen with a special low odor marker.
The queen is kept separate from the hive while the marker dries and the smell wears off. She hides from and dislikes light so the box was turned over after this photo was taken.
What happens to the queen if she has the wrong or not enough odor to stop the hive rebelling? A grisly regicidal spectacle called "balling the queen". Her daughters gang up on her entombing her in a ball of their bodies that smothers and boils her to death. It is a good expression I'm not sure why its not more widely used.