When do we use it? When there are:
a) Relationships between variables
b) Correlation between variables
We will code it like this: PRC.
Unlike experimental statistical tests where it is predicted that there will be differences among scores, Pearson makes predictions about the nature of the association (positive/negative, weak/strong/none) between variables.
Another important bit about correlational statistics like Pearson is that both variables are continuum rather than discrete. This means that interval data can be used in Pearson.
Correlations can be negative (inversely proportional) or positive (directly proportional) thus they are linear, and strong (r > 0.5) or moderate (r <= 0.5 and r > 0.3) or weak (r <= 0.3).
Remainder: correlation does not imply causation. Nice reading about this here.
Final thoughts about Pearson
A coefficient weaker than “weak” is not relevant even if it is statistically significant.
Even when a significant correlation is found between two variables, there are often more than one explanation for the correlation.