A finger bowl is a tiny little bowl, filled with water, for the purpose of rinsing your fingers between courses, especially if said courses involve eating with your hands.
Many cultures still eat with their hands (I’m thinking of Ethiopian and Moroccan off the top of my head). I have never eaten at a restaurant that delivered finger bowls to the table, although I’ve read about them.
We dined at an Asian restaurant recently, and the first thing brought to the table, after the menus, was a bamboo cradle holding a steamy, hot towel. I thought for a moment I was in business class on my way to Europe.
Apparently, it isn’t uncommon to receive a hot towel before the meal in many Japanese restaurants, but it was the first time I ever encountered it and I think I kind of like it.