I heard that phrase in a movie once and I’m not sure what it means. It sounds like it could be something sinister.
It could be, and usually is. It’s exactly what it sounds like: someone who “sells” influence (their own or others’). In other words, someone powerful offering favors in return for payment. If you really want to know more, though, I have connections at Merriam-Webster - if you make it worth my while, I could get the real skinny on the definition for you. In fact, for the right price, I could make it mean whatever you want it to mean.
Today an influence peddler is called a “mover and a shaker.”
Seriously, it’s a person who actively seeks bribes to influence politicians, etc.
The context I heard it in was the movie “Constantine” with Keanu Reeves. The John Constantine character used it referring to something evil.
What does “mover and a shaker” refer to? 
Important people. Someone who can make things happen with just a few words in the right ear. Someone with lots of resources at their command. Someone with lots of connections among the rich and powerful. Someone who plays a significant role in shaping the course of the future. It may or may not involve unethical behavior.
If you agree with what they’re doing, you’d call them an astute politician and a good person. If you don’t agree with what they’re doing, they’re a slimeball. The term ‘influence peddler’ definitely implies the latter and that unethical or downright illegal behavior is involved. It probably also implies that they’re not that important, they’re just really good at manipulating people and making a profit from it.
The phrase makes me think of exotic dancers or prostitutes. They move it and shake it, “it” being their cute little money-making derrieres. 
It doesn’t have to be evil. Malcolm Gladwell refers to such people as “agents of change” in The Tipping Point (and then breaks them down into three different types of change agents).
Allied Van Lines and a small group of celibate women.
Anyone who has been Governor of the State of Illinois, why do you ask?
Romney used the term in the Florida debate this evening to describe what Gingrich did with Freddy Mac.
[QUOTE=Policymic]
Romney told the audience that Gingrich was “disgraced by his own party” during his time as Speaker of the House and accused Gingrich of “influence-peddling” during his 15 years since. Romney attacked Gingrich, “You were getting paid by Freddie Mac while they were costing the people of Florida millions of dollars.”
[/quote]
Exactly what I came in here to say.