1) Dinner-table accessory 2) Place setting part 3) Place-setting part 
The napkin ring, occasionally called a serviette ring, was originally used to identify the napkins of a household between weekly wash days. The standard napkin ring is a simple ring made from skewers. The figural napkin ring is an American specialty in which the simple napkin ring is part of a small figure or sculpture that may take any shape and ...
[n] - a circular band used to hold a particular person`s napkin
noun a circular band used to hold a particular person`s napkin
a ring or band of metal, wood, plastic, etc., through which a folded napkin is inserted, often as part of a place setting.