What that plate under your coffee cup is actually for?

When I was young, my grandfather used to pour hot drinks into the small plate to make it cool off faster so that I can have a taste. Well, back then it was tea instead of coffee I’m getting. But that is the only way I’ve seen people using that small plate under the coffee cup. Especially if you are staying in a hot country which it takes a long time for the drinks to cool off, that small plate under coffee cup seems to become very handy in cooling off hot drinks.