WHY USE BOOTIES
Regardless of the type of exercise you do, most of them involve foot contact with the ground, which can be abrasive, or with a support on which your foot will rest (step, bike, trampoline...). Wearing a sock helps to limit friction between your foot and these elements.
FOR AQUABIKE PRACTICE
It's a good idea to wear booties when you go aquabiking, to avoid injuring yourself on the bike pedals (unless they're designed to be barefoot).
During aquabike classes, you often move from a seated to a standing position, and a lot of pressure is put on the pedal with your foot. If you're wearing slippers, they'll cushion your footing on the bike pedal.