FOR AQUABIKE RIDING
It's a good idea to wear slippers 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, with a lot of foot pressure on the pedals. If you're wearing socks, they'll cushion your footing on the bike pedal.
WHY USE BOOTIES
Regardless of the type of exercise you do, most of them involve your feet making contact with the ground, which can be abrasive, or with a support on which your foot will rest (step, bike, trampoline...).
Using a sock will limit the amount of friction between your foot and these elements.