Even the Word Detective isn't sure:

Dear Word Detective: I've heard the word "akimbo," but I never knew what it meant until someone said "legs akimbo," so I now know it means "spread apart." But where does "akimbo" come from? -- Ben, via the internet.

"Akimbo" is one of the strangest words in the English language, and seems almost to have been invented to mystify folks, especially children. I remember reading many stories as a child in which various characters were described as standing with their "arms akimbo," and being utterly clueless as to what the term meant. Of course, after a little while it dawned on me that I was growing up in a house awash in dictionaries and so I looked it up, but it still strikes me as a very odd word.

For those readers who still haven't figured out what the word means, the late John Ciardi gave a vivid definition of "akimbo": "With hands on hips and elbows sharply bent outwards, a body posture indicating impatience, hostility or contempt." One of the odd things about "akimbo" is that, strictly speaking, the word only applies to this "hands on hips" stance, although metaphorical uses are occasionally seen, such as "legs akimbo" or even "mind akimbo."

The origins of "akimbo" are a bit obscure, but it most likely comes from the Old Norse "i keng boginn," meaning "bent in a curve" (the Norse "bogi" is also the source of our "bow"). The phrase entered English around 1400 as "in kenebow," and then spent the next few hundred years mutating through forms such as "on kenbow," "a kimbow," "a kenbo" and "a-kimbo" until it finally arrived at its modern hyphenless "akimbo" form.
W.D.