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The margin of error is the statistical number that defines the chances that a sample differs from its population. It is used as a theoretical concept in mathematics, and is widely used in any form of research, usually political or sociological, that requires extrapolating information from a limited amount of subjects onto a larger population.

Since this is election season, and the most common place that people will encounter the phrase "margin of error" is in the context of political polling, I will talk about that application of the concept, rather than the mathematical formalism, which I don't have the knowledge to speak on anyway. In most political polls in the United States with a realistic sample size (between 500 and 1500 people, usually) the margin of error is between 3 and 5%. Since most American elections, both on the whole and in the states that are most important in the electoral college, are decided by a smaller percentage than that, most polls are not conclusive sources of information. They are usually only useful in the context of other polls, or of the previous electoral history of a state.

The other thing to remember about a reported margin of error is that a margin of error is a mathematical formalism, that defines the chance of error in a truly randomly selected sample. The margin of error is what is left over when a poll has otherwise perfected its methodology. In practice, in political polls, even the most conscientious, least biased polling organizations have less-than-perfect methodologies. Everything from when to call, to how many questions to ask, to whether a call uses a live person or a recording can skew the answers somewhat. Therefore, the mathematical margin of error may be secondary to the non-technical "margin of error" introduced by methodology.

So, a "margin of error", in political polling, is a technical way to describe the known unknowns. However, it is always best to remember that along with that, there are also many unknown unknowns.

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