Possibly an ideogrammic compound (會意): a 犬 (“dog”) guarding four 口 (“vessel”) – containers, or a phonetically borrowed character for the modern meanings with the original meaning being “to bark” (Compare 狺).
Often used interchangeably with 機(ki) in compounds to indicate “machine”, with the subtlety that 器 implies a smaller device, perhaps hand-held, while 機 implies a larger machine, such as an airplane. Compare 食器(shokki, “tableware”) and 飛行機(hikōki, “airplane”), or homophones機械(kikai, “machine”, generally larger) and 器械(kikai, “machine, tool”, generally smaller).
From Old Japanese. Cognate with 空(utsuo, ancient utsupo, utsubo), signifying a hollowness. Appears to be a compound of 空, 内(utsu, “hollow”, combining form, standalone form uchi, “inside”) + は(ha). The derivation of this ha element is unclear.