S is the test statistic for the Friedman test. Under the null hypothesis, the chi-square distribution approximates the distribution of S. The approximation is reasonably accurate when either the number of blocks or the number of treatments in the randomized block design is greater than 5.
Minitab uses the test statistic to calculate the p-value, which you use to make a decision about the statistical significance of the terms and the model. The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.
A sufficiently high test statistic indicates that at least one difference between the medians is statistically significant.
You can use the test statistic to determine whether to reject the null hypothesis. However, using the p-value of the test to make the same determination is usually more practical and convenient.