Which of course literally means: "I am a jelly-filled sugar donut." I think on one of the shots of Kennedy saying that, you can see Willy Brandt sitting behind him with a slightly puzzled expression on his face.
It mean that around as much "I'm Danish" mean that I'm saying "I'm Danish pastry". To make it even more complex a Berliner Pfannkuchen is not called a Berliner in Berlin (I think it's called a Pfannkuchen), through in Lübeck where Willy Brandt was from it is called a Berliners. So everybody was fully aware what Kennedy was saying, and yes Brandt may have found the sentence slightly funny, but for the Berliners the meaning would have been clear.