It's an old English idiom. It means the uncanny ability to turn anyone around in an argument — in other words, high persuasive ability. It means someone who is extremely persuasive. read more
A more common description, meaning this, is “He [or she] could talk the hind legs off a donkey”. Example of use: “I expected that I’d have to pay a large fine, but my lawyer could talk the stripes off a zebra, and I got off”. read more