Futons are a space saving alternative to traditional mattresses and bedding. The use of futons first originated in Japan during the Edo era (1603-1868), as a means to utilize space the most efficiently while offering totally comfortable and supportive bedding.
The Japanese style of futon, which is in use as beds to this day in Japan, consists of mattress (shikibuton), pillow (makura), mattress cover and quilt (kakebuton). These futons were designed to be used on tatami flooring and are traditionally folded up during the day for ease of storage.
Pictured above is a traditional futon folded for storage (left) and laid as bedding on the floor (right)
The Western style of futon mattress is often thicker, often reaching upwards of 8 to 10 inches, and features a wider range of ingredients, including foams, latex, memory foams, and in some case, springs (recently, there has been a rise of using natural ingredients for these mattresses, including latex memory foam and hybrid soy-based foams which replace some of the petroleum used to make foam with soy bean oil). Western futon mattresses are traditionally housed on a folding wooden frame that can function as bed, but also fold up for use as a sofa. They are usually sold as a set that includes mattress, cover and frame, though be advised that in many cases these components are sold separately as well.
There are many different style of frames, from the conventional bifold futon model, to the a frame, to futon loveseats. These types of futon frames are described in depth here. Additionally, there are wall hugger futon frames that convert from bed to couch with out ever leaving the wall, increasing ease of use and being potentially less damaging on floors and walls. These futon frames are described in depth here.