The BBC provides this explanation and definition of the term:
The vast majority of parliamentarians do not hold ministerial or shadow ministerial office and are known as backbenchers. They are so-called because they sit on the back benches of the Commons or Lords – ministers and their opposition counterparts sit on the front benches.
The OED cites a first British use in 1910, and more than a century later it’s unavoidable in the U.K. and other countries with a Parliamentary system. But it took a long time for Americans to start to use the the term to refer to their own politicos. The moment finally arrived in in 1988 (at least in the archives of the New York Times), and the person who used it was none other than Representative Newt Gingrich, who had filed ethics charges against Speaker of the House Jim Wright. Gingrich (whose fondness for another Britishism has been covered on this blog) was quoted in the Times as saying: ”If Jim Wright were a backbench member, I probably wouldn’t have done anything…. But he’s the Speaker, and everything he could have done all his life as a backbencher becomes self-destructive when he becomes third in line to be President of the United States.”
The first time a Times reporter called an American a backbencher was four years later. Now it’s a commonplace. Four of the last six times the term’s been used in the Times have been in reference to Americans, most recently a January, 5, 2013, Ross Douthat column in which he noted that Speaker John Boehner’s “own backbenchers blew up his attempt at a fiscal cliff negotiating maneuver.”
It’s a useful term, but it bit less potent than in the U.K. since here, it’s not only metaphorical but untrue: since 1913, members of the U.S. House of Representatives have been allowed to sit anywhere they want.