If you are going to eat using your fingers (a very medieval practice), using a serviette (or at a pinch a tea towel), prevents getting nasty hard to remove grease stains on your garb from the roast chicken and making the hospitaller angry if you borrowed the garb. Some etiquette sources specify a large napkin, draped over the diner's left arm.
The other, and more period option of cleaning your face and removing greasy bits from your hands and mouth is using the tablecloth. Yes - that's what they're there for! Don't be afraid, they're going to get washed anyway. Another period option, which is less likely to enrage the owner of the tablecloth, is to use the napkin for your mouth and to wipe your fingers on the innards of a piece of bread.