As you know, the Student t-test can be used only to compare two groups. When you have k groups you can't use a t-test for each couple because, if you have fixed alpha=0.05 for each t-test, there is a probability of k*0.05 to find a difference when it isn't (Bonferroni inequality).
The Holm-Sidak test is a step-down "recursive reject", because it applies an accept/reject criterion on a sorted set of null hypothesis, starting from the lower p-value and going up to the acceptance of null hypothesis.
For each comparison, the alpha value is set according to Sidak correction of Bonferroni inequality.
Statistics Toolbox is required because this function use TCDF function.