A kotatsu is a Japanese traditional heating device which is essentially a square or rectangular coffee table with a heater installed underneath, covered with a futon-like blanket. It is used mostly in the winter season. There are many kinds of kotatsu, for example, a dug kotatsu, a put kotatsu, an electric kotatsu, etc...
It was first used during the Muromachi period about 660 years ago. It became popular amongst a Zen sect, who used a charcoal burner to produce the heat. Now most kotatsu have infrared heaters that won't burn if accidentally touched.
Since many Japanese homes do not have central heating, the sight of friends, family and even pets sitting around a kotatsu has often been a familiar site in anime.
Relevance to Urusei Yatsura
Kotatsu are a common sight in Urusei Yatsura which many of the characters have inside their homes. It is of particular significance when it concerns the character of Kotatsu-neko who is obsessed with these heater tables. He's usually seen sitting with his paws under one, in Ataru's room, in the Principals office, and just about everywhere. He even has a kotatsu with him whenever he's outdoors (although I don't know where he plugs it in).