Definition: an election district that has many fewer inhabitants than other election districts with the same voting power
Political contests, particularly those that go on for an extended period of time, have the ability to popularize certain words and phrases that would otherwise remain fairly obscure. A clear example of this occurred on April 6th, 2016, when the word rotten borough spiked in lookups.
Online articles used the political term to refer to both Donald Trump and Hilary Clinton:
But the estimated 58 percent of delegates he needs to win the nomination remains feasible if he wins big in the Northeast and remains sufficiently competitive in California to win some rotten-borough congressional districts mainly populated by minority folk who are feared and resented by their few Republican neighbors.
—New York Magazine, 6 April 2016
She won two elections in what was a large rotten borough in New York....
—National Review, 6 April 2016
Rotten boroughs initially were election districts that had become largely (or entirely) depopulated, yet retained the right of representation. The term was originally exclusive to Britain; the existence of these sparsely inhabited districts was greatly diminished by the Reform Acts of 1832 and 1867.
The earliest evidence for a borough being called rotten comes from 1761, found in a four-page pamphlet with a wonderfully splenetic title).
From such corrupting and bribing in poor rotten Borough Towns hath followed the Establishment of numberless Places and Pensions, out of the Property of the People, to gratify such Men as can discover Infallability in every Minister, and therefore always vote for the Measures of those who get Places, Pensions, or other Gratuities for them.
—The Rotten and Tottering State of the Popular Part of the British Constitution Demonstrated, Joseph Massie, 1761
As may be seen by the examples from New York Magazine and The National Review, rotten borough is today used in a fairly figurative fashion, referring simply to electoral districts which have a degree of representation that is incongruous with their population. There is no evidence to suggest that these districts actually have anything rotten or putrescent about them.