Dojangs have various training floor surfaces; some modern, some traditional. Each surface has advantages and disadvantages.
Wood is a traditional floor surface. Wood is hard and provides little cushioning, but it provides good support for stable stances. It is easy to pivot and spin on wood, but this becomes more difficult as sweat makes the wood either sticky or slippery. Wood may warp, crack, or splinter over time if not properly constructed or maintained.
Tatami is a traditional floor surface for martial arts such as Aikido and Judo. Tatami is tightly woven rice straw. They have about the same cushioning as a hard foam mat. Cushioning is important when doing falls. Tatami are rarely used outside the orient. Straw tatami is expensive to purchase and maintain, so synthetic substitutes are used where the use of tatami is desired but not financially practical.
Hard Surface/Soft Base
This type of surface has a base of used car tires spread over the floor with a two-by-four wood framework covered with plywood placed atop the tires. The plywood is then covered with a thin pad and a canvas sheet. This type of surface is hard and very stable, but still offers good cushioning.
There are many types of mats. Single sheet synthetic mats are fairly stable, and are usually temperature sensitive (hard when cold, soft when warm). When soft, toes may snag and cause injury. When hard, they lose some of their cushioning. They may get sticky with use and require sprinkling with powder. Stability requires subtle movements in the joints when may either strengthen the points or lead to joint damage over time. Old multiple section horsehair mats get hard with age and do not stay together very well. Multiple section soft mats tend to separate at the joints. Falling directly on a joint may lead to injury, also toes may snag in the joints. Mats kept folded may mold if not aired often. Multiple sheet hard mats with interlocking joints offer cushioning, good traction, stable surface, and the joints stay together rather well. When used on a carpeted floor, the interlocking mats tend to gradually slide in the direction of the nap of the carpet and must be re-centered regularly.
Training outside on grass creates a feeling of being a real warrior, but it is dirty and hidden objects may cause injury so shoes may be required.
Carpet is a terrible training surface. It is hard, holds moisture and odors, and causes carpet burns on exposed skin. Many newly opened schools start with carpet until they can afford a better surface.
Concrete is probably the worst surface. It has no cushioning and is difficult to keep clean. It is usually only found in clubs where they meet in whatever facility they can acquire.