Saponification is a process that applies hydrolysis of a fat in basic environment.
For that often animal fat is used. This fat suffers hydrolysis, and than the products glycerol and fatty acids are formed.

This way we can saponificate palm oil, and in basic environment the produced fatty acid is transformed into Sodium palmitate (a salt!). In fact, this is soap.
If as a base, we do not use NaOH, but KOH, the salt Potassium palmitate will be formed and this soap is softer.