Titten is a colloquial and somewhat crude German word for "breasts" or "tits." While it might seem provocative, it's a very memorable and central word in this Rammstein song.
In the context of the song, the narrator is explicitly stating his desire for a woman with "dicke Titten" (big tits), making it a key, if not the key, theme of the lyrics. Its directness and prominence make it an unforgettable word for learners.
This song tells the story of a lonely man whose life has become dull and gray. He feels like he's losing his mind and his hair, and his only comfort comes from his small dogs. He desperately wants to find a female partner to share his life with.
However, his list of requirements for this partner is surprisingly simple and specific. He states that he's not picky at all. She doesn't need to be beautiful, smart, or rich. In fact, he doesn't even need her to kiss him or feed him grapes. The narrator's one and only request, which he repeats throughout the song, is that she must have "dicke Titten," or big breasts. The song uses this humorous and blunt desire to paint a satirical picture of a lonely man's priorities.