One suggestion is that it comes from the Icelandic word keng-boginn, "crooked", but there is no evidence that keng-boginn ever meant anything other than "crooked", or that akimbo ever meant simply "crooked". Also, if this theory of the origin of akimbo is correct, there should be an earlier English form such as *keng-bow, but no such word exists.
Other suggestions trace akimbo to another Middle English word, cambok, "a curved stick or staff" (from Medieval Latin cambuca) or to a cam bow, "in a crooked bow". However, there is no extant form of akimbo spelled with cam; and the earliest form of the word, kenebowe, is a long way from cam. The bo part of the word is presumably related to bow, but no connection has ever been documented.
The Middle English Dictionary, with some noted uncertainty, proposes that akimbo might be related to Old French chane or kane "pot" or "jug" respectively, combined with Middle English boue, "bow". In that case, the word akimbo originally meant "bent like the handle of a jug"; however, there is no evidence for this, either.
Until recent times (the 1980s or thereabouts), the term was almost exclusively arms akimbo, with little involvement of the legs; it seems that it was first creatively used to describe sitting cross-legged. More recently, the term has been adapted still further, giving a second sense of limbs being splayed out rather than merely bent.
In the late 1990s and 2000s, the word was adopted into computer gaming, where the meaning was modified until it referred to the dual wielding of two weapons. For example, in a first person shooter game, the player might choose a "pistols akimbo" option to wield one gun in each hand.
During the 1990s the phrase gained comic notoriety in the UK when comics The League of Gentlemen used it for the name of a children's educational theatre company, Legs Akimbo.