This is what I found:

The word “okay” has circled the globe and entered common parlance in dozens upon dozens of languages. Its meaning is flexible, being used in the following situations:
• To agree, as in “Okay, let’s do that.”
• To describe something as lacklustre: “The food was just okay.”
• To suggest something as acceptable. “You did an okay job.”
No historian or linguist precisely knows the first origins of the word. Some point to similar meanings in Greek, Choclaw (the tongue of a Native American people), and several African languages. The word first garnered acceptance in the US; so could have come from immigrants, native peoples, or slaves imported from Africa during the 1700 or 1800s. Whatever its origins, “okay” became popularized during the 1840 US Presidential election, and then quickly spread the globe.

The truth is, sometimes we simply don't know where a certain expression or phrase comes from. The best we can do is find the earliest examples of usage and look at the context from that.  At the same time, beware of the many silly explanations that people like to make up - it won't help you at all.

I usually trust Gary Martin's work on phrases.org.uk - he does a lot of thorough research, and is happy to dismiss the sillier explanations.

www.phrases.org.uk/meanings/okay.html