Testing Seasonality

In testing seasonality, you look through all the t-statistics until you bump into an extremely large one, which is the month with the seasonality effect. The explanation says that there is an extremely large autocorrelation here. From what i understand, autocorrelation is the correalation of the ERROR term with the previous error term., but it says that when there is one error in one period, the next period will see movement in the error term in the same direction. So when there is seasonality, shouldn’t this affect the correlation coefficient? This seasonality effect should affect the outcome, so it should be the coefficient. Can someone explain this to me by drawing the formula and make it step by step?

you find to see if error terms are correlated on the past

then you take those period and find out again

in most of the terms, we have dependencies at last and 4th last (same qtr) of the year.