What is meant by the three handfuls of water? Does it mean that the hand should be wet with water three times and wiped with it over three different areas of the scalp, or what?

The "hathyat" (handfuls) in ghusl refer to scoops or handfuls, meaning the amount of water that fills both palms. The person performing ghusl washes their head with these three times.

As for a woman whose hair is braided, she is not required to undo her braids. Rather, it suffices for her to wash and rub them to ensure water reaches the roots and follicles of the hair. This is based on the Prophet's (peace be upon him) statement to Umm Salama: "No, it is enough for you to pour three handfuls of water over your head, then pour water over the rest of your body, and you will become pure."