A cloth napkin.
Even the most well-mannered people can't help but leave some particles of food around their mouth. It's natural, and our ancestors probably didn't mind it very much, wiping their mouths clean with their arm or their shirt. But that would be impolite at the dinner table, wouldn't it? Instead of the tablecloth, your arm, or your fancy business suit, just grab a cloth or paper napkin, carefully dab around your mouth until it's clean enough to be reasonable, and then put it back on your lap. Oh, and do not blow your nose or wipe your brow with it, ever! Excuse yourself from the table and use the bathroom instead. Please.
Disposable paper napkins are commonly found in napkin holders in cafes and informal restaurants, while washable cloth napkins at high-class restaurants are often found in empty glasses before the meal begins, and should be placed over the lap as soon as the guests are seated.