"craftsman who makes barrels, tubs, and other vessels from wooden staves and metal hoops," late 14c. (late 12c. as a surname), either from Old English (but the word is unattested) or from a Low German source akin to Middle Dutch cuper, East Frisian kuper, from Low German kupe (German Kufe) "cask, tub, vat," which is from or cognate with Medieval Latin cupa (see coop (n.)).
A dry cooper makes casks, etc., to hold dry goods, a wet cooper those to contain liquids, a white cooper pails, tubs, and the like for domestic or dairy use. [OED]
As a verb, "to make barrels, casks, etc.," 1746. The surname Cowper (pronounced "cooper") preserves a 15c. spelling.