"What do you have for breakfast?"
Translation:Что у тебя на завтрак?
Russian often leaves out the word "is" in the present tense, which can be confusing for English speakers because "есть" can mean "is" or "have" in different contexts. In this context, Russians would never say that you have something. They would say that something is for you and "есть" is optional, even unnecessary.
From what I've learned, есть is used when asking about the existence or presence of a thing or person. Here the question is about the process of having breakfast.
This is reinforced by the fact that завтрак is in accusative case rather than prepositional case: words which follow the preposition на which involve static location are cast in prepositional case, but it is cast in accusative case where the word after на means or concerns "onto or on when movement is involved OR "for + [circumstance/activity] (such as "for breakfast")". Here the existence or presence of something isn't in question, so есть isn't required.
According some charts of prepositions I've located, a noun which is the object of the preposition на is Accusative when на "means 'on to, on' when movement is involved" or Prepositional when it "means 'on, in, at' to define location".
на завтрак doesn't seem to fit either of these qualifications. There have been several exercises using на in Prepositional case when it was used to describe something going on on a bed, making the location of the activity the most significant part of determining case, so I'm not certain that "breakfast" could be interpreted as some kind of process - "breaking the fast" (what it literally means) by eating, or "breakfasting", engaging in eating breakfast, similar to the verbs "to dine" or even "to lunch".
This use of на seems extremely particular and limited in possible use - or is it more common than I am thinking?
In English, this use of "for" seems to involve a concept which includes activity. "For lunch" "for the holidays". Google Translate returned <<Мы идем в дом моих родителей на Рождество> as a translation of "We go to my parents'house for Christmas"
In typing in the English text, I notice that Google was using для until I finished typing in "Christmas", at which point, Google changed для to на.