early 14c. (late 12c. as a surname), pouche, "bag worn on one's person for carrying things," especially (late 14c.) "small bag in which money is carried," from Anglo-French puche, Old North French pouche (13c.), Old French poche "purse, poke," all from a Germanic source (compare Old English pocca "bag;" see poke (n.1)). Extended to sac-like cavities in animal bodies from c. 1400.
1560s, "put in a pouch;" 1670s, "to form a pouch, swell or protrude," from pouch (n.). Related: Pouched; pouching.