Where did the phrase "OK" come from?

No one knows for sure but the strongest argument for its etymology is explained by Columbia University professor Allen Walker Read.

The letters stand for 'oll korrect' (all correct), the result of a fad that started in Boston newspapers in 1838. It gained national fame when supporters of Martin Van Buren adopted it as the name of their political club in 1840 ('Old Kinderhook,' giving 'OK' a double meaning). Opponents used it against him, saying that it had originated with Van Buren's allegedly illiterate predecessor, Andrew Jackson, and came up with other interpretations: Out of Kash, Out of Kredit, and Out of Klothes.

Soon, newspaper editors and publicists around the country created their own meanings: Oll Killed, Orfully Konfused, Often Kontradicts, etc. By the time the campaign ended, the expression 'OK' had spread nationwide.