Definition: As an adverb or adjective, today's word means "all right." When it's a noun, it's an approval, and the verb means "to approve."
Usage: OK is spelled OK, O.K., Ok, or okay. The US astronauts have extended it to A-OK, meaning "absolutely OK."
Etymology: Urban legend has it that Andrew Jackson, with a dubious grasp of written English, spelled "all correct" as "oll korrect." Another assigns "OK" to a World War II body-count system which included 0K (zero + K), meaning "zero killed," implying that everything is all right. But OK entered English well before the 1940s. Allen Read claims that the word entered American English in the Boston Morning Post in March of 1839 during a fad of acronyms and abbreviations, including OFM (Our First Men), NG (no go), and SP (small potatoes). Apparently, it was the scenesters' jargon of the time. As scenesters tried to establish an even more "elite" vocabulary for the in-crowd, facetious spellings began to appear, with NG turning to KG (Know Go). OK came from that silly spelling "Oll Korrect." By autumn, 1840, the term had traveled from New York to New Orleans via the popular press, and during the Van Buren campaign, OK was used to take advantage of the acronym game to refer to "Old Kinderhook," an extension of the name of Van Buren's birthplace in the Hudson Valley, Kinderhook.
Fonte: Dr. Language, YourDictionary.com