OK, a little cornball humor to begin the post.
What is soap?
According Wikipedia, "soap is an anionic surfactant used in conjunction with water for washing and cleaning, which historically comes either in solid bars or in the form of a viscous liquid." And that is clear as mud.
Soap is the reaction of glycerides (fatty esters) with sodium hydroxide (strong alkaline solution). The process is called "Saponification." Vegetable oils (lipid materials derived from plants) and animal fats (rendered tissue fats that are obtained from animals) are fatty esters in the form of triglycerides. Sodium Hydroxide (NaOH), also known as lye or caustic soda is a caustic base. The alkali breaks the ester bond and the product of the reaction is glycerol and fatty acids. Fatty acids in the soap emulsify the oils in dirt, enabling the removal of oily dirt with water.
Sodium hydroxide comes in pellets, flakes, and granular form. It absorbs water from the air and should be stored in an airtight container. It is very soluble in water and heats up to over 200 degrees in a matter of seconds. Solid sodium hydroxide or solutions of sodium hydroxide will cause chemical burns, injury or scarring, and blindness if it contacts unprotected human tissue.
Sodium Hydroxide, or Lye, is nothing to fool around with. Protective equipment such as rubber gloves, safety clothing and eye protection should always be used. It reacts with certain materials so it should only be mixed in glass or plastic, never aluminium.
You might have someone tell you there is not any lye in their soap. Don't be fooled. What they mean is they use a soap base and melt it and pour it into molds. There is no actual saponification occurring in the process. The soap has already been made, with lye, by someone else.