Okay is a term of approval or assent, often written as OK. When used to describe the quality of a thing, it denotes acceptability. However, its usage can also be strongly approving; as with most slang, its usage is determined by context.
The word "okay" is currently posited as the single most used word on earth, owing to its common employment in a vast number of cultures and languages.
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There is some dispute over the origins of this word.
There is a Choctaw word "okeh" with the same meaning and pronunciation as American usage; Woodrow Wilson, among others, used this spelling to emphasize the Native American origins of the word. The Choctaw language was well known as a lingua franca of the frontiersmen of the early 19th Century, including eventual American Presidents Andrew Jackson and William Henry Harrison.
It is said that Andrew Jackson, when asked about his usage of the two letter acronym on bills, responded that OK stood for "oll korrect," a phonetic misspelling of "all correct."
Allen Walker Read
Allen Walker Read wrote six articles in the journal American Speech in 1963 and 1964 on the origins of the word. He dismissed the Choctaw origins as mythic folklore, emphasizing the possibility that "OK" arose as a cute abbreviation.
He believed the word to be short for any of several different spellings of "all correct", including "Oll Korrect", "Orl Korrect", and "Ole Kurreck". There was a fad in the 1830s and 1840s involving the intentional misspelling of common phrases, and referring to them by the resulting initials. These may have been infuenced by the Plattdeutsch/Low Saxon phrase "Oll klor", which would have been spoken by emigrants from Northern Germany. The fad included many other briefly popular abbreviations such as OW, "oll wright" (all right) and KY, "know yuse" (no use), none of which have survived. The first recorded use of "OK" in this sense was in the Boston Morning Post on March 23, 1839, in the sentence "He...would have the 'contribution box', et ceteras, o.k.--all correct--and cause the corks to fly, like sparks, upward."
Read discounts evidence of earlier popular origins of the word, for instance, a Boston businessman used it in a daily journal in 1815.
Another etymological claim made for the origin of "okay" is the influx of native Africans, along with their language, into the United States in the years of slavery in the latter country. It is claimed that the phonetic "waw-kay" is a phrase (or word) in either the Bantu or Wolof dialects (or both), "kay" being a word meaning "yes," and "waw" an emphatic; "waw-kay" is an emphatic "yes." To lend credence and weight to this claim are additional co-options of native Bantu and Wolof words, such as: "jev" for "jive"; and "banana," among others. It is claimed that the now morphed English phonetic "okay" was backronymed so as to be attributed to other languages (such as German or English), and may have been used as a political tool to gentrify the attitudes of the poor and uneducated by making them think they knew a "fancy" upscale acronym that politicians use. 
In the presidential election of 1840, the term "OK" was further popularized by use as an slogan by the O.K. Club, New York boosters of Democratic president Martin Van Buren's 1840 re-election bid; it was an allusion to his nickname Old Kinderhook, from his birthplace Kinderhook, New York. Van Buren lost, but the word stuck. 
Whatever its origin, it spread around the world, the "okay" spelling of it first appearing in British writing in the 1860s. Spelled out in full in the 20th century, 'okay' has come to be in everyday use among English speakers, and borrowed by non-English speakers. Occasionally it is extended to okey dokey or even, thanks to Ned Flanders, okely dokely.
Since the term bears resemblance to a person's initials, many proposals have been made as to who "O.K." was, and why their name would become synonymous with acceptability.
One theory says it comes from a railroad freight agent, Obadiah Kelly, who initialed bills of lading, or an Indian chief Old Keokuk who wrote his initials on treaties. Another theory is that it comes from boxes of Orrins-Kendall crackers which were popular with Union troops during the US Civil War. Some say the term comes from a German businessman Otto Kaiser who put his initials on goods he had inspected. A related version ascribes it to a worker named Otto Kruger or Oskar Krause at a Ford plant in Michigan, who would inspect each car coming off the assembly line and chalk his initials on the front windshield if it was "OK".
Other Uses and Possible Explanations
The term OK has also been used in an English will and testament from 1565. It is possible that this usage originates from "oak" the tree from which British Navy ships were constructed at the time of the British colonization of North America and the subsequent War of Independence. The actor David Garrick (1717-1779) wrote the Royal Navy's song "Heart of Oak", a patriotic song celebrating naval victories of the Seven Years War (1756-1763). In Britain oak wood is a symbol of solid dependable construction. Thus it is possible to see how establishing the reliability of the vessel might involve asking if it was "oak-a?" In 2000 the First Sea Lord, Admiral Sir Michael Boyce said, in the Royal Navy's "Navy News": "It is no exaggeration to say that the reputation of the Royal Navy is founded on British oak."
The term OK was also used by typesetters and people working in the publishing business. A manuscript that didn't need any changes or corrections would be marked "O.K." for Ohne Korrektur (German for "No changes"). In ancient Greece teachers would mark especially good school papers with "OK" for Ola Kala (Ολα Καλά, ΟΚ), meaning that everything is good; as a variant on that theory, the Greek phrase would be used by sailors as a quick way of responding to the captain's inquiry about the condition of the ship. Another theory is that it comes from the British English word hoacky (the last load of the harvest). Or the Finnish word Oikein (that's right). Or the Scottish expression och aye. Or the French aux Cayes or au quai. Or a word used in many west African languages meaning all right, yes indeed and introduced in the US via slaves.
A surely apocryphal account is that the term was used in U.S. military records to state that there were zero casualties or zero killed, hence 0.K., at a particular battle site.
Whether this word is printed as OK, okay, or O.K. is a matter normally resolved in the style manual for the publication involved. Common style guides: Chicago, New York Times, etc., provide no consensus nor do dictionaries.
From Oxford dictionary, okay (also OK) / adj, adv (informal) all right; satisfactory or satisfactorily Eg. I hope the children are okay. I think I did OK in the exam. He is OK happy.
- Webster's Dictionary of English Usage, Merriam-Webster, 1989.