Since you usually had several people digging into a common dish with their fingers, having clean hands was important. People were advised by the "Miss Manners" of the day to wash their hands out in the open where everyone could see and then be assured your hands were clean.
Of course, it was another matter to keep your hands clean during the meal. In the Middle Ages and Renaissance, manuals for manners gave a list of things people should refrain from during a meal, such as:
Other bad manners advised against were: people blowing their noses or wiping off sweat with their napkins; people poking around on a plate (probably looking for the better piece of food) and putting bones back on a platter after eating the meat off. We would consider their "proper" place for bones - the floor- pretty crude today! The "release of wind" was also frowned upon.