In such constituencies and boroughs, due to the small number of electors, the post of Member of Parliament could effectively be bought. Because the constituencies were not realigned as population shifts occurred, MPs from one borough might represent only a couple of people (giving those people a relatively large degree of political representation), whereas entire cities (such as Manchester) might have no representation at all. Examples include: Old Sarum in Wiltshire had eleven voters, Dunwich in Suffolk had 32 voters, Plympton Earle with 40 voters, and Newtown on the Isle of Wight with 23 voters (all figures for 1831). All of these boroughs could elect two MPs. At one point, out of 405 elected MPs, 293 were chosen by less than 500 voters. (Spielvogel) Many such rotten boroughs were controlled by peers who 'gave' the seats to their sons, they thus having influence in the House of Commons while also holding seats themselves in the House of Lords. The Duke of Wellington, prior to being awarded a peerage served as MP for the rotten borough of Trim in County Meath in the Irish House of Commons.
In addition, there were boroughs where parliamentary representation was in the control of one or more 'patrons' by their power to either nominate or other machinations, such as burgage. Patronage and bribery were rife during this period. In some cases, wealthy individuals could "control" multiple boroughs -- the Duke of Newcastle is said to have had seven boroughs "in his pocket". In the 19th century measures began to be taken against rotten boroughs, notably the Reform Act of 1832 which abolished most rotten boroughs and spread parliamentary seats based on population, not past history of parliamentary representation. The introduction of the secret ballot helped prevent patrons from controlling districts, as they could no longer examine an individual's vote prior to its casting, electors as a result for the first time having the freedom to cast votes as they, not their landlord, wished.
Today, "rotten borough" is sometimes used to refer to a parliamentary constituency in which one particular political party has such massive support that its candidate is effectively uncontested. It is also used to refer to allegedly corrupt branches of local government - Private Eye has a column entitled Rotten Boroughs which lists stories of municipal wrongdoing.
"[Borough representation is] the rotten part of the constitution." -- William Pitt the Elder
See also: gerrymander