Schlesinger is talking about the "mass organizations" of the communist parties. Those were actually fronts for the communist parties that would, many times, attract members that were not aware of the political agenda or political mindset of the leaders.
This is a strategy commonly used by communist parties around the world and it's very prominent in South America, specially.
Schlesinger's concern is about the influence that the Communist Party had over those groups and how its power was increasing through groups that "disguised" as something else but were actually under control of the Communist Party and the party could eventually use the individuals that belonged to those groups to achieve their goals and many times, the individuals used wouldn't even be aware of it.
