By being subtle and quietly cunning you may catch even a clever monkey. Trying to do it more obviously by direct means will fail. So it means to be quiet, tactful, cunning, devious even , to persuade somebody rather than loud or direct.

It's usually written as 'softly, softly catchee monkey' as if someone, perhaps Chinese, is speaking pidgin English. People have trouble with the meaning simply because writing 'catchy' causes confusion with 'catchy' as in "that's a catchy tune."

It first appeared in print in a book of quotations published in 1907. Precisely as Fred says above, it is just a proverbial phrase recommending caution and the gentle approach as the best way to achieve an objective.

Didn't they name the TV series Softly, Softly after the phrase too? [Spin off from Z-Cars with Stratford Johns & Frank Windsor?] A sort of early sweeney without the firearms & punchups? Like Dixon compared to the Bill? [showing my age now] the first to ask what did you do in the war gets '

well but what did you???