It's a type of sqrt decomposition technique, generally we can solve such problems by taking 2 cases (heavy and light), for eg. if we classify vertices in a graph based on it's degree we can see that as the number of edges is bounded by M (say), we know that there won't be many (at most sqrt(M)) heavy vertices with degree more than or equal to sqrt(M), and we can use brute force for the light vertices. You can watch the tutorial video by Errichto.