If someone gives you a notification, like you have to do something, or you have to go out and get some thing, and you say "ok". What are you doing? Would 'acknowledge' be the proper word to describe your action?
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...and you say "ok". What are you doing?
Well, without explaining yourself further, only you know what you are doing.
OK can indicate a number of other things as well. It can even indicate disagreement or ridicule depending on how it's said.
"Acknowledge" is insufficient. Because as a response to a request "okay" includes "I accept" or "I approve", "agreed" or "will do" would be better. (Of course, "okay" as affirmation or qualitative commentary could be replaced with "satisfactory", "adequate", sufficient", or "palpable". It is not so positive as many English students believe.)