When interacted, the chemical reaction called Saponification occurs. The end result turns once greasy oils into soap which cleans you.
Soap is very unusual acting like a snake with two heads.
The fatty head hates water and the alkali head loves water. Glycerine is in fact more valuable by weight then soap. Milled soaps remove their glycerine by adding salt to their batch. Most glycerine in turn is used as a stabilizer in Food and Cosmetics production, as well as an inhibitor in cigarette paper which allows it to burn more evenly. This soap base is made transparent by using alcohol, sugars, heat and pressure.