The original clawfoot bathtub was a heavy cast-iron tub that stood off the floor on four metal feet. The interior of the tub was enameled and the feet were gilt, and made to resemble animal feet, most often the paws of a lion.
In the 1880s, John Kohler (whose company eventually came to bear his name) had a foundry that made farm equipment. He took a traditional horse trough shape and added an enamel coating to make it easier to keep clean. The result was impressive enough that he advertised it in his catalog as "a horse trough/hog scalder, when furnished with four legs will serve as a bathtub."
American Standard had a similar product at about the same time; who originated the design is difficult to ascertain.
The basic shape is a long bowl with a lip that curved back on itself; this formed the smooth rim of the tub. If one end of the tub is higher than the other end, it is called a 'slipper-style' clawfoot. The high, sloping back is designed for reclining in the water for relaxation, so these are also called 'soaking tubs'.
The footed tub was standard bathroom equipment for decades. Built-in bathtubs are relatively recent innovations, meant to lessen cleaning time - who wants to mop under the tub, after all? Tubs were soon being made out of acrylics and fiberglass and not out of metal or porcelain. These are significantly less heavy, easier to install and cheaper.
Many people are now looking for a more traditional design for their bathroom furnishings, and the major manufacturers are now supplying them with clawfoot tubs again, both in metal/enamel and in acrylic. While the original clawfoots came in white, you can now buy a clawfoot to match any decor. Two tone models (the inside being a different color than the outside) are also available. Some models have the water fixtures in the center and both ends high and sloped for reclining, so that couples can soak together.
Add a few candles, turn out the harsh overhead lights, add a few drops of Jasmine oil to the bathwater and you can turn the clawfoot bathtub into a sensual spa retreat.