It’s not that it was needed to “fill a gap” in any language. Before 1839, English speakers had “yes”, “good”, “fine”, “excellent”, “satisfactory”, and “all right”.

What OK provided that the others did not was neutrality, a way to affirm or to express agreement without having to offer an opinion.

Consider this dialogue: “Let’s meet again this afternoon.” Reply: “OK.”

Compare that with: “Let’s meet again this afternoon.” Reply: “Wonderful!” or “If we must.”

http://www.bbc.co.uk/news/magazine-12503686