In the 19th and 20th centuries in southern and western America, there were traveling shows that had singers, acrobats, comics/clowns, actors, dramatic speakers, etc. They were the only entertainment some villages would ever have, since people were poor and transportation was difficult and expensive. Part of the show was men selling "medicine" that they claimed would cure all kinds of diseases and problems. Most of the time, it was just alcohol with a few herbs in it; however, these men were very skilled salesmen, and would usually make a lot of money at each performance (luckily, they were far away by the time the victims realized they had bought something worthless!).
So the phrase, "medicine-show man" is a way of describing someone who sells you something he knows is not going to really help you; or, as a way of describing someone who is a very good salesman or who has a very persuasive way of talking. It is not a compliment!