The correlation statistic presents the first instance in which we'll be examining statistical significance. The question is whether we can reject the null hypothesis (Ho) that the correlation between a given pair of variables in the full population is zero (RHO = 0).

We, of course, obtain correlations (r) for our sample, and then see if our sample correlation is sufficiently different from zero (in either a positive or negative direction) so that it would have been sufficiently unlikely to have arisen from pure chance when the population RHO was truly zero. Under that situation, we can reject the Ho of zero RHO.

This article by Jerry Dallal provides a concise historical summary of why p < .05 has become the "magic" cutoff point.

Some of my postings from recent years (here and here) address statistical significance with correlations in additional ways.