The previous answer does a good job of describing the differences between British and American ideas on representation today, but I have noticed that all of Newkirk7’s questions seem to concern the colonial period in American history. This is true of the questions posted today and those posted on past days. Therefore, I will answer with that interpretation of the question in mind.
In late colonial times, there was a distinct difference between American and British ideas. The British believed in the idea of “virtual representation.” What this meant is that they accepted the idea that not all men would get a chance to vote for their representatives. They argued that all people would be represented simply because members of Parliament would have their best interests in mind. In other words, the members of Parliament would be like parents who would do the right thing for their “children” (the constituents) even if the children had no say in the matter. The British argued that American colonists were represented in this way and did not need to actually vote for members of Parliament. By contrast, the American colonists felt that representation could only exist (for white men with property, at least) if they were actually able to vote for their representatives. This is known as the dispute between “virtual representation” and “actual representation.”
The British and American perspectives on representative government are products of their unique histories and political evolutions.
Unlike the United States, which is a relatively new country, Great Britain's history goes back many centuries. Its evolution as a parliamentary form of government is a result of growing disenchantment with the rule of the Crown. One of the most important documents in British and, by extension, American history is the Magna Carta, or the The Great Charter of the Liberties of England of 1215. The Magna Carta, produced by prominent citizens of England, represented the first successful effort at restricting the power of the monarch, King John. By proscribing the king's authorities in such a document, the path was clear for the development of representative government. The evolution toward full democracy was far from complete, but the evolution had begun. The British parliamentary system that exists today represents the culimination of that evolution.
The American system of representative democracy is vastly different from that of the British. Under the British parliamentary system, citizens vote for political parties more than for individual politicians. The party that wins or carries a district represents that district in parliament. The party that holds the most seats in parliament elects a prime minister from within its ranks. That prime minister serves as both leader of his or her party and as leader of the government.
Under the parliamentary system, elections can be held whenever the distribution of seats allows for a shift in the balance of power within the parliament. Another feature of parliamentary systems is the ability of small parties to hold power out of proportion to their representation in parliament. Because a party needs a majority to form a government, if it doesn't have that majority of seats it must form an alliance with one or more smaller parties until it is able to secure a majority of votes for the position of prime minister. While common in some parliamentary systems around the world, the British House of Commons, the lower but more influential of its system, the House of Lords being the other, is almost always governed by either the conservative, or Tory, party or by the liberal, or Labor, party.
The Founding Fathers of the newly independent United States were heavily influenced by their knowledge of the evolution of British government. Because Britain still had a powerful, if no longer all-powerful, king, the drafters of the U.S. Constitution adopted a presidential system of government in which a Chief Executive would preside over the government, but with his powers checked by a Legislative Branch of government that would have authority over the budget, over the power to declare war, over the making of laws, and over the ratification of international treaties. In addition, a Judicial Branch of government would ensure that laws passed by Congress and signed by the Chief Executive did not run counter to the words and intent of the Constitution.
Representation of the public was intended to be greatest in the House of Representatives, which alone has the authority to originate legislation to "appropriate" or spend money. The Senate -- intended to be a little less representative -- alone can confirm presidential nominees for high-level positions and to ratify treaties.