In biochemistry, starch is a polymeric carbohydrate (a polysaccharide), in which the monomers are glucose units joined to one another usually head-to-tail. The overall structure is not, however, simply a linear polysaccharide chain, since occasionally, two glucose units are joined to one, forming a branch point.
Animal starch is the common name of glycogen. It is not the same as ordinary starch.
Clothing starch or laundry starch is a liquid that is prepared by mixing a vegetable starch in water (earlier preparations also had to be boiled), and is used in the laundering of clothes. During the 19th century and early 20th century, it was stylish to stiffen the collars and sleeves of men's shirts and the ruffles of girls' petticoats by applying starch to them as the clean clothes were being ironed.
Aside from the smooth, crisp edges it gave to clothing, it served a practical purpose as well. Dirt and sweat from a man's neck and wrists would stick to the starch rather than fibers of the clothing, and would easily wash away along with the starch. Then, after each laundering, the starch would be reapplied.
See also the article on how to make starch from frosted potatoes from the 1881 Household Cyclopedia.