When snapping fingers, the loud click comes from the finger hitting the palm. The friction of the thumb and finger rubbing together makes only a faint brushing sound, which comes just before the sound of the snap.
This explanation is testable by snapping but not allowing the finger to contact the palm. Alternatively, padding, such as an adhesive bandage, a tissue or the cuff of a sleeve, could be placed over the palm. With this protection in place, the sound of the snap is significantly deadened.
Snapping fingers is not difficult, but rapid repetition is challenging. According to Guinness World Records, the most finger snaps in one minute is 278. This record was set in 2008 by Jens Gudmandsen of Sweden.