아침/점심/저녁 드셨어요? (honorific)
식사하셨어요? (honorific, more common)
밥 먹었어? (casual)
They all literally means "Did you have breakfast/lunch/dinner?". Eating 밥(meaning rice, breakfast/lunch/dinner) is very important for Koreans, so you can take it as a Korean way of saying "How are you?". Some people don't bother to say anything like that and just start a conversation directly talking about what's going on in their life.
Something funny about it is, when my mom says the phrase and hear me say I ate some bread or something westerners eat, she says "밥 먹어야지" even though I'm full.