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What is a correlation coefficient?

What is a correlation coefficient? Here are some definitions.

Noun
  1. (statistics) Any of the several measures indicating the strength and direction of a linear relationship between two random variables.
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Examples
The reliability coefficient may be interpreted as a correlation coefficient between this measurement and a hypothetical remeasurement taken under similar conditions.
Researchers sample populations over a range of latitudes to calculate a correlation coefficient between body size and latitude for a particular species.
The absolute value of the correlation coefficient represents the strength of the association between the two variables.
The Spearman rank correlation coefficient was computed to assess correlation between continuous variables.
The Kappa coefficient is the statistical parameter used for ordinal data and the intra-class correlation coefficient for continuum data.
Most often when we compute a correlation coefficient between two variables, we take observations on both variables.

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