I'm a bit confused about what "drikker" means? I know that the sentence means "What are you drinking?" , so do drikker and drinking mean the same thing?
Yes. Notice how there is an "er" (are) at the end. It's the same with if you wanted to say the woman you would say kvinnen and the word "the" would attach to the end instead of before like in English. So it's kind of the opposite of English so instead of saying is drinking you literally translate drikker to English it would be "drink is".
drikker means "are drinking/is drinking/drink" han drikker vann = he is drinking water jeg drikker øl = i drink beer (or i'm drinking beer) du drikker vin = you drink wine