If you are not following this conversation series here the previous post.
Let us assume that we have two processes, for each of which we measure some set of parameters. As a result, we get a set of pairs of numbers (process 1 and process 2 parameter values). Assuming that these processes are somehow related, we assume that this relationship should reveal itself numerically in the values of the parameters. Therefore, we can somehow get information about the presence or absence of the relation from the resulting number of pairs.
However, the relationship can be of different strength, so it is desirable to obtain not a binary “yes” or “no”, but a kind of continuous number that will characterise the degree (strength) of the relationship between the two variables. And now, meet the Pearson correlation coefficient.