Correlation: A correlation is a statistical index used to represent the strength of a relationship between two factors, how much and in what way those factors vary, and how well one factor can predict the other. Using correlations does NOT (I repeat, does not) provide you with cause and effect information; it will not tell you if one factor causes or is caused by the other.
This fact was an important component in the court cases against the tobacco companies that occurred in the late 1990's. The studies conducted previously on the effects of smoking indicated a positive correlation between smoking and cancer. This means that the studies found that as the rate of smoking increased, so did the occurrence of cancer; smoking goes up, presence of cancer goes up. BUT, this does not demonstrate that smoking causes cancer (does anyone disagree that it does?), only that there is a relationship between the two factors.
See also: Positive Correlation and Negative Correlation