A Kotatsu is a low table combined with a futon and a heating source.
In Japan the Kotatsu is one of the traditional symbols of the winter season. A kotatsu generates heat underneath the table surface. The table surface is attached on top of a kind of blanket or futon. Of course, the idea is to put your legs underneath the blanket to warm yourself. This relates to the fact that Japanese houses traditionally are not very well insulated and can be quite drafty.
The kotatsu, as a symbol of the winter season, is traditionally linked to another symbol of winter: the mikan. This is a fruit similar to an orange but is smaller and is perhaps more akin to a tangerine. The mikan is thus considered to be a variant of the mandarin orange (just like the tangerine). In Japan, the mikan is associated with winter because of the fact that it is filled with necessary vitamins for the winter season. However, there is something particular that links the mikan and the kotatsu, apart from their primary association with the winter season. The mikan is a fruit to be peeled, of course. And as such it is thought to generate a pleasant group activity; that is to say, the peeling and eating of the mikan is considered to be something best enjoyed with company. Now, the kotatsu is often the center piece of a family's home in the winter season. Japanese houses are generally very small and often have only one available room that is used as the living and eating room. Therefor, the kotatsu is often a place of gathering for the family. Not only does the kotatsu itself warm the members of the family, but, of course, the family members warm each other with their presence. Combine this with the mikan and it should be obvious that they facilitate a gathering of the family and also generate the right conditions for good conversation and overall family bonding.
Traditional Japanese houses used to have a kind of open fire place in the center of the most important room; it is called an 'iori'. This fire place was usually the only heat source in the house and was also used for cooking. In a way, it could be argued that the kotatsu is an evolved form of that fire place sans the cooking function.
In Persona 4 the kotatsu is featured as part of the Dojima residence. The link with the mikan fruit is also mentioned, however, in the English version of the game mikan is simply localized as orange.