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The correlation between two sets of data is a measure of how close they are to making a straight-line graph.

A measure of association (co relation) between two random variables X and Y.
Usually the term correlation means the Pearson correlation coefficient, which is a measure of linear association.
There are other coefficients of correlation, such as the Spearman rank correlation coefficient which is a measure of monotonic association.
If two variables tend to move up or down together, they are said to be positively correlated. If they tend to move in opposite directions, they are said to be negatively correlated. If r is 0, X and Y are said to be uncorrelated.
Corelation does not mean causality. Two variables can be highly correlated without having any causal relationship, and two variables can have a causal relationship and yet be uncorrelated.
Independent variables are always uncorrelated, but uncorrelated variables need not be independent.