Although you will see decoration for western food, definitely Japanese cuisine has more decorations which is possible to eat.
Probably the most frequent one is when you ordered sashimi. Sashimi will not be served in front of you with just slices of raw fish. There are several garnishes, usually are daikon radish and green shiso which are placed under the fish slices.
Due to those garnishes are possible to eat but those are not for eating together with sashimi. Daikon are sliced in thin pieces and it is for reducing the bad smell from the fish meat and keeps the sashimi fresh. Green shiso is also told to keep sashimi fresh. Therefore, daikon and green shiso must be placed under the sashimi.
Actually eating these daikon and green shiso is up to the people. However, people say eating these garnishes are polite against chefs who prepared the dish.