"drink" is present tense, but in the past tense: "did drink" = "drank" and the form with "did" for past and "do" for present is used in questions when the conjugated part of the verb is before the subject in English.
Do you drink? I drink.
Did you drink? I drank.
What did you drink? I drank rootbeer. Yes, they served it in a beer stein. I bet you thought I had a beer. I guess they didn't want me to feel left out, but I was the designated driver. What do you mean you don't believe me? I did drink rootbeer!
Which brings us to another use of this auxiliary or helping verb, the negation is "I did not drink." for the past and "I do not drink." for the present as well as the possible contractions "don't" and "didn't".
As you can see, "did drink" and "do drink" can also be used for emphasis in a regular sentence to answer a negation with a little indignation that they would not believe you. Little kids often say "did not" "did too" back and forth.
If it said, what did the students drinking, that would be plain wrong in English. It would have to be, what did the students drink. I guess the latter is a one-off completed action, whereas your version is continuous and (assuming there's an imperfect tense in Spanish, which I haven't got to yet) would need an imperfect tense.