Tom yum is a classic Thai spicy soup that is served hot. A tom-yum pan is how it's kept hot when it's brought to your table. There are many variations to this pan, but this is a common shape. Below it, is placed a source of heat, I use an oil burner, but more commonly a special burning tray is used, a charcoal burner, or burning embers from a fire.
A variation of it is used for Isan Suki Yaki; the Isan variation of the Japanese dish. For that variation, the centre is solid - there is no hole in it, meat is fried on the centre section and the juices drain into the soup as it cooks.
You can also use tealight candles with this pan to keep soup hot, but candles can only be used to keep food warm, not cook it.
And my final tom yum pot. This one is perfect for herbs, some herbs react with the metal pans and this is a great way to serve those.