According to the story, the animal fat from the animals that were sacrificed in the fire to the Roman gods ran down the sides of the altar and mixed with the ashes of the fire. In time this goopy mess found its way down to the banks of the Tiber River where women would do laundry by pounding the dirt out with rocks.
What the women found was that dirt was easier to get out if the goopy mass was applied to the fabric first. The first miracle cleaner had been discovered by accident at a place near a hill called "Sapo". And so the Roman historian Pliny, gave this "gross confection" the same name as the hill. In time "sapo" became our modern word "soap". Romans only used soap in the laundry. They never used it on the skin because it was crude stuff and it could damage the skin.
Soap is made by cooking fats and oils with toxic materials such as lye, caustic soda or potash. In order for the result not to be well... disgusting, you must have just the right amount of each ingredient. Too much of one raw material and the soap is greasy and won't lather. Too much of another ingredient and the soap is grainy and strong.
As with all things, people began to specialize in the manufacturing of soap. The best soaps were known to come from the Castile region of Spain, where olive oil instead of animal fat as used in the making of the soap. The wealthy classes in Europe used Castile soap for hundreds of years.
In the American colonies, people made their own soaps at home. They made lye by mixing burnt wood ashes with water in a bucket. The lye dripped out of holes drilled in the bottom of the bucket. They got the fat they needed from the butchering of livestock. The animal fat was melted and mixed with the lye until it formed soap. As you can imagine, it was a nauseating (and dangerous) process. In America, the first commercial soap making companies came on the scene in the early 1800s. People were happy not to have to make their soap anymore and these early soap entrepreneurs were very successful