A correlation between two variables measures the strength of the linear relationship between them. Put simply, two variables are positively correlated to the extent that individuals with relatively high or low values on one measure tend to have relatively high or low values on the other, and negatively correlated to the extent that high values on one measure are associated with low values on the other.
Correlations are used frequently in the debate about teacher evaluations. For example, researchers might assess the relationship between classroom observations and value-added measures, which is one of the simpler ways to gather information about the “validity” of one or the other – i.e., whether it is telling us what we want to know. In this case, if teachers with higher observation scores also tend to get higher value-added scores, this might be interpreted as a sign that both are capturing, at least to some extent, "true" teacher performance.
Yet there seems to be a tendency among some advocates and policy makers to get a little overeager when interpreting correlations.