Definition: Saponification is an exothermic (gives off heat) chemical reaction that occurs when fats or oils (fatty acids) come into contact with lye (a base.) Saponification literally means "turning into soap" from the root word, "sapo", which is Latin for soap. The by-products of the saponification reaction are glycerin and soap.
Oils + lye (dispersed into water) = soap + glycerin
Oils and fats each have what is called a “saponification value”, which is the amount of lye needed to completely neutralize them into soap with no lye left over. Each oil has a different value.
Taken from about.com on Candle and Soapmaking
To learn about cold-process soap making, follow the links: http://candleandsoap.about.com/od/soapmakingbasics/g/saponification.htm
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