Saponification is the chemical reaction that happens to oils and fats when combined with lye (a strong alkali) to create soap. Water is used in this process, but only as a carrier for the lye, which is a powder.
Basically, you add lye to oils, which turns the oil into soap. At the end of the process the lye is all gone, and you are left with just soap (and a little bit of oil for moisturizing purposes – see superfatting below).
This is a great article with further information about saponification and soap-making:
They also make this great point about why you should consider handmade soap as a much better alternative to commercial:
“A curious fact about modern soap is that most common soap found in the grocery store made in mass-produced factories does have a small amount of excess alkali in it. Also, it has had all of its naturally-occurring glycerin removed so it can be sold as a separate commodity. Why? Greater profit.”
Excess alkali (lye) is irritating to the skin. There should be enough oils to alkali ratio for all of the alkali to be changed into soap, leaving nothing irritating for your skin.
Glycerin is left in all of my handmade soaps, keeping it naturally moisturizing. Also, there are more oils/fats in my soaps than lye/alkali, which is called, “superfatting.” By adding more oils/fats to my soap recipes than needed to exactly change all of the lye into soap, you make a soap that is more moisturizing and gentler on the skin.