Hi @kiara!
Kruskal-Wallis can be applied to two or more groups, so it can be applied in a pairwise manner (i.e. comparing two groups at a time), or to all groups simultaneously. alpha-group-significance uses the Kruskal-Wallis test for both "all groups" and "pairwise" tests.
Kruskal-Wallis is a non-parametric version of the one-way ANOVA test. Just as ANOVA can be applied to 2+ groups and is a generalization of the t-test (which works with 2 groups only), Kruskal-Wallis can be applied to 2+ groups and is a generalization of the Mann-Whitney U test. See this Wikipedia page for more details. Hope this helps!