saucer
A small plate that is use to support cups, more specifically teacups.
The saucer is useful to protect surfaces from possible damage due to the heat of a cup, and to catch overflow, splashes, and drips from the cup, so protecting both table linen and the user sitting in a free standing chair who holds both cup and saucer. It can also be an area to place your damp spoons.
Often comes along with a tea_set especially when being served to others.