I talked to my brother earlier and was unable to accurately describe a kotatsu so I took some pictures to use as visual aids.
This is a whole and complete kotatsu. It's made up of a table, a futon, and a zabuton which is a futon that goes under the table on the floor.
This is a picture of the zabuton with a cushion on top of it that you sit on and the large futon lifted up. You sit on the cushion and cover yourself with the big futon. It's very snug and warm.
This is a picture of underneath my kotatsu. The heater's is on the bottom of the table. The cord leads to a switch.
This is the switch. You can turn the heater on and off with it. The temperature control for the heater is on the side of the heater itself so you can control the temperature from just warm to really, really hot.
This is a better if slightly sideways picture of the heater. You can see the temperature knob.
The heater shoots out heat which is then trapped by the encasing futons and then you can put your feet and part of your legs under the table and get all toasty warm.
I hope that this has been a helpful description of a kotatsu.