Simply put, saponification is the process between lye and fat that creates soap. Sodium hydroxide (NaOH) can be used with fats to create a hard soap. Potassium hydroxide (KOH) can be used to create liquid soaps.
Above is a lightly saponified soap, while below is one that has saponified faster due to the mixture of fats. Like a high school chemical experiment, the fats are the acid (fatty acids) and the lye is the base in the chemical reaction . Each fat requires a certain amount of base to saponify. As the reaction continues the triglycerides in the fats (acid) release the glycerol molecule. The glycerol molecule is what becomes the glycerin that makes cold process soap so wonderful for your skin! After the single glycerol molecule is released, the remaining fatty acids combine with the base to become soap.
The easiest way to remember this:
Fatty acid (fats, oils) + Lye (NaOH or KOH) = Glycerin & Soap
After the beginning to saponify soap batter is spooned into the molds it is set aside on a shelf to continue the saponification process for the next 24 hours. During this time the soap will self heat as a result of the chemical reaction and continue to process. After 24 hours the pH drops significantly, and within a short amount of time there is no longer an acid or base remaining, just skin nourishing cold process soap full of naturally created glycerin!