I think that Kennedy is referring to the presence of Cuban communism with Fidel Castro in his Democratic National Convention address in 1960. The idea of "communist influence has penetrated" is something that Kennedy had to bring out as a major part of his campaign to show to Americans that he was not "soft" on the Communist presence around the world. Senator Kennedy had to point out that American attention must be given to the Communist influence around the world because of the perception that he and other Democrats were "soft" on the presence of Communism, something that Nixon never had to fight through in his campaign. In suggesting that the "Communist influence" in Cuba had to be addressed, Kennedy is raising the issue that he will focus on Communism everywhere in the world should he be elected President. This is something that Kennedy and his advisers felt important enough to be included in his convention speech accepting the Democratic nomination for President, and something that was believed to be important enough to deliver on this stage introducing him as a candidate to rival the Republican Nixon.