Have no idea where it came from, but it means that if you tread carefully and don't go in guns blazing then you're more likely to get what you want (i.e you wouldn't catch a monkey by running up behind it yelling and waving your arms about)
It's usually written as 'softly, softly catchee monkey' as if someone, perhaps Chinese, is speaking pidgin English. It first appeared in print in a book of quotations published in 1907. It is just a proverbial phrase recommending caution and the gentle approach as the best way to achieve an objective...as others suggest above.
young cow to older cow " Hey look, the bulls are coming" Older cow " Don't get your hopes up, one will be too knackered when he gets here and the other one will have forgotten what he came for"