A third rail is an issue that politicians and officials don’t want to touch because it’s too controversial. The idiom refers to the actual third rail used in electric rail systems. The third rail carries a high voltage, so touching it is extremely dangerous.
Third rail is originally American. The Oxford English Dictionary lists a couple of examples of third rail used metaphorically from the early 20th century, but the political sense did not emerge until around 1980. In many older instances, third rail is embedded in the longer third rail of American politics or just third rail of politics. Today, those longer forms are less common.
The phrase is still most common in American publications, but it is known outside the U.S. and appears regularly.
Examples
One item in the Obama administration’s fiscal 2013 defense-spending request could hit a third rail with military voters: changes to military pay and benefits. [Wall Street Journal]
[I]f Republicans thought social security was a third rail, contraception is the fourth. [Washington Post]
In the same way that social security is viewed as the “third rail” of American politics, the NHS has long been regarded as untouchable. [Guardian]
Conflicts of interest, which used to be the third rail of journalism, now seem to have become like herpes instead. [Globe and Mail]
You know what they say: Diapers are the third rail of baby politics. [Huffington Post]
Other resources
William Safire on “Third Rail” in the New York Times Magazine