Literally, "I am a pastry".
Do a search on Google for "berliner brot" for lots of nice german pastry recipes.
When I was taking German--years ago--in high school, our teacher pointed out that this famous line of Kennedy's actually translated as "I am a jelly doughnut", and that the proper translation for "I am a citizen of Berlin" would have been "Ich bin Berliner." Style over substance, a la WJC.
Does anybody else here have any German background, that could verify the translation?