"deep vessel for carrying liquids, usually with a handle or ear," late 15c., jugge, variant of jubbe (late 14c.), a word of unknown origin. Perhaps it is from jug "a low woman, a maidservant" (mid-16c.), a familiar alteration of Jug, a common personal name such as Joan or Judith.
Use as a musical instrument is attested from 1886 in jug-band (American English) "musical ensemble in which the bass line is carried or augmented by a player blowing on the open lip of a jug. "As a quantity of ale or beer, a jug is usually a pint" [Century Dictionary, 1902].
representing the sound of the nightingale, 1530s.