Correlations are a great tool for learning about how one thing changes with another. Correlation values closer to 0 are weaker correlations, while values closer to positive or negative 1 are stronger correlation. (Source)

In statistics, the Pearson correlation coefficient (PCC) ― also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data.It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1 (-1 ≤ r ≤ 1). (Source)

The "r value" is a common way to indicate a correlation value. More specifically, it refers to the (sample) Pearson correlation, or Pearson's r. The "sample" note is to emphasize that you can only claim the correlation for the data you have, and you must be cautious in making larger claims beyond your data. (Source)